New Approach to Study Numeric Triangles

Abstract

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 T2

References
[1] Graham R L, Knuth D E and Patashnik O 1989 Concrete Mathematics(MA: AddisonWesley)


[2] Stanley R P 1999 Enumerative Combinatorics 2(Cambridge University Press)


[3] Lando S K 2003 Lectures on Generating Functions(American Mathematical Society)


[4] Barry P 2011 J. Integer Seq.14 11.4.3


[5] Shapiro L W, Getu S, Woan W-J and Woodson L C 1991 Discr. Appl. Math.34pp 233–249


[6] Merlini D, Sprugnoli R and Verri M C 2006 Acta. Appl. Math.94pp 229–239


[7] Kruchinin D V and Kruchinin V V 2013 J. Math. Anal. Appl.404pp 161–171


[8] Kruchinin V V and Kruchinin D V 2014 J. Anal. Num. T. 2pp 1–8


[9] Kruchinin D V and Kruchinin V V 2012 J. Integer Seq.1512.9.3


[10] Kruchinin D V and Kruchinin V V 2015 J. Integer Seq.1815.4.6


[11] Barry P 2013 J. Integer Seq.16 13.5.1


[12] Banderier C, Krattenthaler C, Krinik A, Kruchinin D V, Kruchinin V V, Nguyen D and Wallner M 2017 Explicit formulas for enumeration of lattice paths: basketball and the kernel method(Developments in Mathematics Series Springer)