%0 Journal Article
%T Generalization of Stirling Number of the Second Kind and Combinatorial Identity
%A Ji Peng
%J Open Access Library Journal
%V 7
%N 6
%P 1-6
%@ 2333-9721
%D 2020
%I Open Access Library
%R 10.4236/oalib.1106462
%X <div style="text-align:justify;">
	The Stirling numbers of second kind and related problems are widely used in combinatorial mathematics and number theory, and there are a lot of research results. This article discuss the function:  
‘<i>A<sup>C<sub>1</sub></sup><sub style="margin-left:-15px;" "="">1</sub></i> <i>A<sup>C<sub>2</sub></sup><sub style="margin-left:-15px;" "="">2</sub></i> ，，，<i>A<sup>C<sub>k</sub></sup><sub style="margin-left:-15px;" "="">k</sub></i> (C<sub>1</sub> C<sub>2</sub> ，，， C<sub>k</sub>=N-K, C<sub>i</sub>−0), obtain its calculation formula and a series of conclusions, which generalize the results of existing literature, and further obtain the combinatorial identity: ‘(-1)<sup>K-i</sup>*C(K-1,K-i)C(A-1 i,N-1)=C(A,N-K).
</div>
%K Combinatorics
%K Combinatorial Identity
%K Stirling Numbers
%K Calculation Formula
%U http://www.oalib.com/paper/5435719