Stoll, Michael Bounds for the length of recurrence relations for convolutions of P-recursive sequences. (English) Zbl 0880.11017 Eur. J. Comb. 18, No. 6, 707-712 (1997). Let \(S_r(n)\) denote the sum of the \(r\)th powers of the binomial coefficients \({n \choose k}\), where \(0\leq k\leq n\). Franel’s conjecture states that \(S_r(n)\) satisfies a linear recurrence of length \([{1\over 2} (r+1)]\), where the coefficients in the linear recurrence are polynomial functions of \(n\). The author proves Franel’s conjecture, as well as a more general theorem. Reviewer: N.Robbins (San Francisco) Cited in 1 ReviewCited in 2 Documents MSC: 11B37 Recurrences 11B65 Binomial coefficients; factorials; \(q\)-identities Keywords:binomial coefficients; Franel’s conjecture; linear recurrence PDFBibTeX XMLCite \textit{M. Stoll}, Eur. J. Comb. 18, No. 6, 707--712, ej960123 (1997; Zbl 0880.11017) Full Text: DOI