20 citations · 29 across the 11 of their papers we have counts for
4 papers · 1 filter
Integer properties of a composition of exponential generating functions
Dmitry Kruchinin
In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite num…
Application of a composition of generating functions for obtaining explicit formulas of polynomials
Vladimir Kruchinin, Dmitry Kruchinin
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated L…
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Vladimir Kruchinin, Dmitry Kruchinin
We present techniques for obtaining a generating function for the central coefficients of a triangle , which is given by the expression $[xH(x)]^k=\sum_{n\geqslant k} T(n,k…
The number of multinomial coefficients based on a set of partitions of n into k parts and divided by k evenly
Dmitry Kruchinin
In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with…