Divisibility of Certain Classes of Stirling Numbers of the Second Kind

摘要

In this paper, we introduce and prove an alternate formula of Stirling numbers of the second kind as We have obtained some results of p-adic valuations of S(p~2, kp) for 2 < k ≤ p - 1, S(2p,p - 1),S(2p,p), S(2p,p + 1) and S(2p,p + 2) and also expressed in terms of congruence mod p~2. The generalization of the p-adic valuations and congruences mod p~2 of S(p~n, kp) for 2 ≤ k ≤ p - 1 and S(2p~n, k) for k = p -1,p are also presented.