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In this paper we deal with numerical triangles defined by generating functions in the power of k. We present new approach to study such triangles that allow us to get methods for obtaining generating functions of the diagonals of the triangles. Methods for obtaining generating functions of the central coefficients and the diagonal T 2 , of the triangle T , are discussed. Some further ideas for application are given. Publishing services provided by Knowledge E Dmitry V Kruchinin. This article isdoi:10.18502/keg.v3i4.2252 fatcat:aywmvr5gmve5jmrsbivxhaovea