Asymptotic Expansions

Abstract

1. Introduction. Let a 1 a 2 , …, a m be a set of real non-negative numbers and let 1.1 P (x) = a 1 x + a 2 x 2 + … + a m x m (am ≠ 0). Many combinatorial problems can be reduced to the study of numbers B n generated by 1.2 . Some problems of this type were treated by Touchard (7), Jacobsthal (3), Chowla, Herstein, Moore and Scott (1; 2), and the present authors (4).