Editing Stirling number (section)

==Symmetric formulae==

Abramowitz and Stegun give the following symmetric formulae that relate the Stirling numbers of the first and second kind.<ref>{{Citation |last1=Goldberg |first1=K. |title=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables|edition=10th  |pages=824–825 |year=1972 |editor-last1=Abramowitz |editor-first1=Milton |contribution=Stirling Numbers of the First Kind, Stirling Numbers of the Second Kind |location=New York |publisher=Dover |last2=Newman |first2=M |last3=Haynsworth |first3=E. |editor-last2=Stegun |editor-first2=Irene A.}}</ref>

:<math> \left[{ n \atop k } \right] = \sum_{j=n}^{2n-k}  (-1)^{j-k} \binom{j-1}{k-1} \binom{2n-k}{j} \left\{{ j-k \atop j-n} \right\} </math>

and

:<math>
\left\{{n \atop k}\right\} = \sum_{j=n}^{2n-k} (-1)^{j-k} \binom{j-1}{k-1} \binom{2n-k}{j} \left[{j-k \atop j-n } \right] 
</math>