Recurrences for sums of powers of binomial coefficients

T. W. Cusick

doi:10.1016/0097-3165(89)90063-0

Recurrences for sums of powers of binomial coefficients

T. W. Cusick

Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Define S^(r)_n=∑ⁿ_k=0(ⁿ_k)^r(r=1,2,...). An elementary method is given for finding a recurrence for S_n^(r) with [ (r+3) 2] terms. This confirms an 1895 conjecture of Franel.

Original language	English
Pages (from-to)	77-83
Number of pages	7
Journal	Journal of Combinatorial Theory, Series A
Volume	52
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(89)90063-0
State	Published - Sep 1989

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title = "Recurrences for sums of powers of binomial coefficients",

abstract = "Define S(r)n=∑nk=0(nk)r(r=1,2,...). An elementary method is given for finding a recurrence for Sn(r) with [ (r+3) 2] terms. This confirms an 1895 conjecture of Franel.",

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year = "1989",

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AB - Define S(r)n=∑nk=0(nk)r(r=1,2,...). An elementary method is given for finding a recurrence for Sn(r) with [ (r+3) 2] terms. This confirms an 1895 conjecture of Franel.

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Recurrences for sums of powers of binomial coefficients

Abstract

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