A Method for Obtaining Generating Function for Central Coefficients of Triangles

Abstract

We present techniques for obtaining a generating function for the central coefficients of a triangle $T(n,k)$, which is given by the expression $[xH(x){]}^k={\sum }_{n⩾k}T(n,k)x^n$, $H(0)\ne 0$. We also prove certain theorems for solving direct and inverse problems.