Lengyel introduced a sequence of numbers Zn, defined combinatorially, that satisfy a recurrence where the coefficients are Stirling numbers of the second kind. He proved some 2-adic properties of these numbers. In this paper, we give another recurrence for the sequence Zn, where the coefficients are Stirling numbers of the first kind. Using this formula, we give another proof of Lengyel’s lower...

Recently, Zhu [34] introduced a Stirling-Whitney-Riordan triangle [Tn,k]n,k?0 satisfying the recurrence Tn,k = (b1k + b2)Tn?1,k?1 [(2?b1 a1)k a2 ?(b1 b2)]Tn?1,k ?(a1 ?b1)(k 1)Tn?1,k+1, where initial conditions 0 unless ? k n and T0,0 1. Denote by Tn Pnk =0 Tn,k. In this paper, we show asymptotic normality of give an formula Tn. As applications, many famous combinatorial numbers, such as Stirlin...

Recently, the generalized Euler–Genocchi and degenerate polynomials are introduced. The aim of this note is to study multi-Euler–Genocchi which defined by means multiple logarithm generalize, respectively, polynomials. Especially, we express former polynomials, multi-Stirling numbers first kind Stirling second kind, latter kind.