Using the (universal) Theorem for the integer partitions and the q-binomial Theorem, we give arithmetical and combinatorial identities for the complete Bell polynomials as generating functions for the number of partitions ...

In this paper, we show that if P(x) = Pm k=0 akx k is a polynomial with nondecreasing, nonnegative coefficients, then the coefficients sequence of P(x s + · · · + x + 1) is unimodal for each integer s > 1. This ...