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Stirling number
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==Further reading== * {{cite journal|first=Victor|last=Adamchik|url=http://www-2.cs.cmu.edu/~adamchik/articles/stirling.pdf |archive-url=https://web.archive.org/web/20041214001155/http://www-2.cs.cmu.edu/~adamchik/articles/stirling.pdf |archive-date=2004-12-14 |url-status=live|title=On Stirling Numbers and Euler Sums|journal=Journal of Computational and Applied Mathematics|volume=79|year=1997|pages=119–130|doi=10.1016/s0377-0427(96)00167-7|doi-access=free}} * {{cite journal|first1=Arthur T.|last1=Benjamin|first2=Gregory O.|last2=Preston|first3=Jennifer J.|last3=Quinn|url=https://math.hmc.edu/benjamin/wp-content/uploads/sites/5/2019/06/A-Stirling-EnCOUNTer.pdf |archive-url=https://web.archive.org/web/20200910121921/https://math.hmc.edu/benjamin/wp-content/uploads/sites/5/2019/06/A-Stirling-EnCOUNTer.pdf |archive-date=2020-09-10 |url-status=live|title=A Stirling Encounter with Harmonic Numbers|date=2002|journal=Mathematics Magazine|volume=75|number=2|pages=95–103|doi=10.2307/3219141|jstor=3219141|citeseerx=10.1.1.383.722}} * {{cite journal|url=http://www.maa.org/sites/default/files/pdf/upload_library/2/Boyadzhiev-2013.pdf |archive-url=https://web.archive.org/web/20150905120358/http://www.maa.org/sites/default/files/pdf/upload_library/2/Boyadzhiev-2013.pdf |archive-date=2015-09-05 |url-status=live|first=Khristo N.|last=Boyadzhiev|title=Close encounters with the Stirling numbers of the second kind|date=2012|journal=Mathematics Magazine|volume=85|number=4|pages=252–266|doi=10.4169/math.mag.85.4.252|arxiv=1806.09468|s2cid=115176876}} * {{cite journal|first=Louis|last=Comtet|url=http://www.techniques-ingenieur.fr/page/af202niv10002/permutations.html#2.2|title=Valeur de ''s''(''n'', ''k'')|journal=Analyse Combinatoire, Tome Second|page=51|year=1970|language=fr|url-access=subscription}} * {{cite book|first=Louis|last=Comtet|title=Advanced Combinatorics: The Art of Finite and Infinite Expansions|url=https://archive.org/details/Comtet_Louis_-_Advanced_Coatorics|publisher=Reidel Publishing Company|location=Dordrecht-Holland/Boston-U.S.A.|date=1974|isbn=9789027703804 }} * {{cite journal| author=Hsien-Kuei Hwang |title=Asymptotic Expansions for the Stirling Numbers of the First Kind |journal=Journal of Combinatorial Theory, Series A |volume=71 |issue=2 |pages=343–351 |year=1995 |url=http://citeseer.ist.psu.edu/577040.html |doi=10.1016/0097-3165(95)90010-1|doi-access=free }} * {{citation |author-link=Donald Knuth|first=D.E.|last=Knuth| journal = Amer. Math. Monthly | title=Two notes on notation| year=1992 | volume=99 |issue=5| pages=403–422 | arxiv=math/9205211 | doi=10.2307/2325085 | jstor= 2325085|s2cid=119584305}} * {{cite journal|first=Francis L.|last=Miksa|jstor=2002617|title=Stirling numbers of the first kind: 27 leaves reproduced from typewritten manuscript on deposit in the UMT File|journal=Mathematical Tables and Other Aids to Computation: Reviews and Descriptions of Tables and Books|volume=10|number=53|date=January 1956|pages=37–38}} * {{cite book|editor1-first=Milton|editor1-last=Abramowitz|editor2-first=Irene A.|editor2-last=Stegun|chapter-url=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP|title=Handbook of Mathematical Functions (with Formulas, Graphs and Mathematical Tables)|publisher=U.S. Dept. of Commerce, National Bureau of Standards, Applied Math.|series=55|orig-year=1964|year=1972|chapter=Combinatorial Analysis, Table 24.4, Stirling Numbers of the Second Kind|first=Francis L.|last=Miksa|page=835}} * {{cite journal|first=Dragoslav S.|last=Mitrinović|url=http://pefmath2.etf.bg.ac.rs/files/23/23.pdf |archive-url=https://web.archive.org/web/20090617034106/http://pefmath2.etf.bg.ac.rs/files/23/23.pdf |archive-date=2009-06-17 |url-status=live|title=Sur les nombres de Stirling de première espèce et les polynômes de Stirling|journal=Publications de la Faculté d'Electrotechnique de l'Université de Belgrade, Série Mathématiques et Physique|language=fr|issn=0522-8441|number=23|date=1959|pages=1–20}} * {{cite web|first1=John J.|last1=O'Connor|first2=Edmund F.|last2=Robertson|url=https://mathshistory.st-andrews.ac.uk/Biographies/Stirling/|title=James Stirling (1692–1770)|date=September 1998}} * {{cite journal| first1=J. M. |last1=Sixdeniers |first2= K. A. |last2=Penson |first3=A. I. |last3= Solomon | url = http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.pdf |title= Extended Bell and Stirling Numbers From Hypergeometric Exponentiation |year=2001 |journal = Journal of Integer Sequences | volume= 4 | pages=01.1.4|arxiv=math/0106123 |bibcode=2001JIntS...4...14S }} * {{cite journal| first1=Michael Z. | last1=Spivey | title=Combinatorial sums and finite differences |doi=10.1016/j.disc.2007.03.052 | journal=Discrete Math. |year=2007 | volume=307 | number=24 | pages=3130–3146| doi-access=free | citeseerx=10.1.1.134.8665 }} * {{Cite OEIS|sequencenumber=A008275|name=Stirling numbers of first kind}} * {{Cite OEIS|sequencenumber=A008277|name=Stirling numbers of 2nd kind}} {{Classes of natural numbers}} [[Category:Permutations]] [[Category:Q-analogs]] [[Category:Factorial and binomial topics]] [[Category:Integer sequences]]
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