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The Series Sum[n^m x^n, {n, 1, Infinity}] and a Pascal-like Triangle

David Neal
Journal / Anthology

College Mathematics Journal
Year: 1994
Volume: 25
Issue: 2
Page range: 99-101

Recently, a very interesting Pascal-like triangle was described by Callan in a proposed problem for solution [1]. ... Like Pascal's triangle, this triangle has some nice properties and interesting applications. In the mentioned proposed problem, one is asked to show that the sum of the entries in the nth row is n!. The proposer of the problem has also generated this triangle from evaluating the permanents of n-by-n circulant matrices [2]. In this paper, we offer another application of the triangle and derive a closed-form expression for [an arbitrary element in the triangle].

*Mathematics > Calculus and Analysis > Series
*Mathematics > Number Theory