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==References== {{refbegin|30em}} *{{cite journal | last1 = Asai | first1 = Nobuhiro | last2 = Kubo | first2 = Izumi | last3 = Kuo | first3 = Hui-Hsiung | arxiv = math/0104137 | doi = 10.1023/A:1010738827855 | issue = 1–3 | journal = Acta Applicandae Mathematicae | mr = 1831247 | pages = 79–87 | title = Bell numbers, log-concavity, and log-convexity | volume = 63 | year = 2000 | s2cid = 16533831 }} *{{cite journal | last = Aitken | first = A. C. | author-link = Alexander Aitken | doi = 10.1017/S1757748900002334 | journal = [[Edinburgh Mathematical Notes|Mathematical Notes]] | pages = 18–23 | title = A problem in combinations | volume = 28 | year = 1933| doi-access = free }} *{{cite journal|first1=H. W.|last1=Becker|first2=John|last2=Riordan|author2-link=John Riordan (mathematician)|title=The arithmetic of Bell and Stirling numbers|journal=American Journal of Mathematics|volume=70|year=1948|issue=2 |pages=385–394|jstor= 2372336|doi=10.2307/2372336}}. *{{cite journal|first=E. T.|last=Bell|author-link=Eric Temple Bell|title= Exponential polynomials|journal=Annals of Mathematics|volume=35|year=1934|issue=2 |pages=258–277|jstor=1968431|doi=10.2307/1968431}}. *{{cite journal|first=E. T.|last=Bell|author-link=Eric Temple Bell|title= The iterated exponential integers|journal=Annals of Mathematics|volume=39|year=1938|issue=3 |pages=539–557|jstor=1968633|doi=10.2307/1968633}}. *{{cite book | last1 = Bender | first1 = Edward A. | last2 = Williamson | first2 = S. Gill | contribution = Example 11.7, Set Partitions | isbn = 0-486-44603-4 | pages = 319–320 | publisher = Dover | title = Foundations of Combinatorics with Applications | url = http://www.math.ucsd.edu/~ebender/CombText/ch-11.pdf | year = 2006 }} *{{cite journal | last1 = Berend | first1 = Daniel | last2 = Tassa | first2 = Tamir | issue = 2 | journal = Probability and Mathematical Statistics | pages = 185–205 | title = Improved bounds on Bell numbers and on moments of sums of random variables | volume = 30 | url = https://www.math.uni.wroc.pl/~pms/files/30.2/Article/30.2.1.pdf | year = 2010 }} *{{cite journal | last = Berndt | first = Bruce C. | issue = 2 | journal = Asia Pacific Mathematics Newsletter | pages = 8–13 | title = Ramanujan Reaches His Hand From His Grave To Snatch Your Theorems From You | url = http://www.asiapacific-mathnews.com/01/0102/0008_0013.pdf | volume = 1 | year = 2011 }} *{{cite book | last = de Bruijn | first = N.G. | author-link = Nicolaas Govert de Bruijn | page = 108 | title = Asymptotic methods in analysis | publisher = Dover | edition = 3rd | year = 1981 }} *{{cite journal | last = Callan | first = David | arxiv = math/0507169 | issue = 1 | journal = Journal of Integer Sequences | mr = 2193154 | page = 06.1.4 | title = A combinatorial interpretation of the eigensequence for composition | url = https://eudml.org/doc/52955 | volume = 9 | year = 2006 |bibcode = 2005math......7169C}} *{{cite journal | last = Canfield | first = E. Rodney | doi = 10.1016/0097-3165(95)90033-0 | issue = 1 | journal = Journal of Combinatorial Theory | mr = 1354972 | pages = 184–187 | series = Series A | title = Engel's inequality for Bell numbers | volume = 72 | year = 1995 | doi-access = free }} *{{cite journal | last = Claesson | first = Anders | doi = 10.1006/eujc.2001.0515 | issue = 7 | journal = European Journal of Combinatorics | mr = 1857258 | pages = 961–971 | title = Generalized pattern avoidance | volume = 22 | year = 2001 | arxiv = math/0011235 }} *{{cite book|last1=Conway|first1=John Horton|author1-link=John Horton Conway|last2=Guy|first2=Richard K.|author2-link=Richard K. Guy|title=The Book of Numbers|series=Copernicus Series|publisher=Springer|year=1996|isbn=9780387979939|contribution=Famous Families of Numbers: Bell Numbers and Stirling Numbers|pages=[https://archive.org/details/bookofnumbers0000conw/page/91 91–94]|url=https://archive.org/details/bookofnumbers0000conw/page/91}} *{{cite journal|first=G.|last=Dobiński|title=Summirung<!-- "Summirung" is an archaic spelling, and it is the spelling that was used in this title. --> der Reihe <math>\textstyle\sum\frac{n^m}{n!}</math> für ''m'' = 1, 2, 3, 4, 5, …|journal=Grunert's Archiv|volume=61|year=1877|pages=333–336|url=https://archive.org/stream/archivdermathem88unkngoog#page/n346}} *{{cite journal | last = Engel | first = Konrad | doi = 10.1016/0097-3165(94)90038-8 | issue = 1 | journal = [[Journal of Combinatorial Theory]] | mr = 1255264 | pages = 67–78 | series = Series A | title = On the average rank of an element in a filter of the partition lattice | volume = 65 | year = 1994 | doi-access = }} *{{cite book | last1 = Flajolet | first1 = Philippe | author1-link = Philippe Flajolet | last2 = Sedgewick | first2 = Robert | author2-link = Robert Sedgewick (computer scientist) | contribution = II.3 Surjections, set partitions, and words | pages = [https://archive.org/details/analyticcombinat00flaj_706/page/n117 106]–119 | publisher = Cambridge University Press | title = Analytic Combinatorics | title-link= Analytic Combinatorics | year = 2009 }} *{{cite journal | last = Gardner | first = Martin | author-link = Martin Gardner | doi = 10.1038/scientificamerican0578-24 | journal = [[Scientific American]] | pages = 24–30 | title = The Bells: versatile numbers that can count partitions of a set, primes and even rhymes | volume = 238 | year = 1978| issue = 5 | bibcode = 1978SciAm.238e..24G}} Reprinted with an addendum as "The Tinkly Temple Bells", Chapter 2 of ''Fractal Music, Hypercards, and more ... Mathematical Recreations from Scientific American'', W. H. Freeman, 1992, pp. 24–38 * {{springer|title=Bell numbers|id=p/b110240|mode=cs1}} *{{cite arXiv|title=An elementary (number theory) proof of Touchard's congruence|first1=Greg|last1=Hurst|first2=Andrew|last2=Schultz|eprint=0906.0696|year=2009|class=math.CO}} * {{cite book|contribution=Two thousand years of combinatorics|first=Donald E.|last=Knuth|author-link=Donald Knuth|pages=7–37|title=Combinatorics: Ancient and Modern|publisher=Oxford University Press|year=2013|editor1-first=Robin|editor1-last=Wilson|editor2-first=John J.|editor2-last=Watkins}} *{{Cite book |author-link=László Lovász| last=Lovász | first=L. |title=Combinatorial Problems and Exercises |edition=2nd |place=Amsterdam, Netherlands |publisher=North-Holland |year=1993|zbl=0785.05001|contribution=Section 1.14, Problem 9|page=17| isbn=9780821869475 |url=https://books.google.com/books?id=e99fXXYx9zcC&pg=PA17}} *{{cite journal | last1 = Moser | first1 = Leo | author1-link = Leo Moser | last2 = Wyman | first2 = Max | journal = Transactions of the Royal Society of Canada, Section III | mr = 0078489 | pages = 49–54 | title = An asymptotic formula for the Bell numbers | volume = 49 | year = 1955 }} *{{cite journal | last = Peirce | first = C. S. | author-link = Charles Sanders Peirce | issue = 1 | journal = [[American Journal of Mathematics]] | jstor = 2369442 | pages = 15–57 | title = On the algebra of logic | volume = 3 | year = 1880| doi=10.2307/2369442}}. *{{cite journal | last = Rota | first = Gian-Carlo | author-link = Gian-Carlo Rota | doi = 10.2307/2312585 | issue = 5 | journal = [[American Mathematical Monthly]] | mr = 0161805 | pages = 498–504 | title = The number of partitions of a set | volume = 71 | year = 1964 | jstor = 2312585 }} *{{cite journal | last = Spivey | first = Michael Z. | issue = 2 | journal = Journal of Integer Sequences | mr = 2420912 | page = Article 08.2.5, 3 | title = A generalized recurrence for Bell numbers | url = http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Spivey/spivey25.pdf | volume = 11 | year = 2008 | bibcode = 2008JIntS..11...25S }} *{{cite journal | last = Wagstaff | first = Samuel S. | author-link = Sam Wagstaff | bibcode = 1996MaCom..65..383W | doi = 10.1090/S0025-5718-96-00683-7 | issue = 213 | journal = [[Mathematics of Computation]] | mr = 1325876 | pages = 383–391 | title = Aurifeuillian factorizations and the period of the Bell numbers modulo a prime | url = http://homes.cerias.purdue.edu/~ssw/bell/bell.ps | volume = 65 | year = 1996 | doi-access = free }} * {{cite book | last=Wilf | first=Herbert S. | author-link=Herbert Wilf | title=Generatingfunctionology | edition=2nd | location=Boston, MA | publisher=Academic Press | year=1994 | isbn=0-12-751956-4 | zbl=0831.05001 | url = https://www.math.upenn.edu/~wilf/gfology2.pdf }} *{{cite journal | last = Williams | first = G. T. | journal = [[American Mathematical Monthly]] | jstor = 2305292 | doi = 10.2307/2305292 | mr = 0012612 | pages = 323–327 | title = Numbers generated by the function ''e''<sup>''e''<sup>''x''</sup> − 1</sup> | volume = 52 | year = 1945 }} {{refend}}
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