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: ∑AC11 AC22 ···ACkk (C1+C2+···+Ck=N-K, Ci≥0), obtain its calculation formula and a series of conclusions, which generalize the results of existing literature, and further obtain the combinatorial identity: ∑(-1)K-i*C(K-1,K-i)C(A-1+i,N-1)=C(A,N-K).