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A371882
a(n) = Sum_{k=0..n} binomial(n,k)^7 * (1 - 7*k*(H(k) - H(n-k))), where H(n) is the n-th harmonic number.
1
1, -5, 109, -3317, 121501, -4954505, 216867925, -9981053045, 476860000285, -23451310381505, 1180189308268609, -60519806861966105, 3152285573768063461, -166371462775232899553, 8880340127444426907109, -478649327347386225075317
OFFSET
0,2
LINKS
Robert Osburn, Armin Straub, and Wadim Zudilin, A modular supercongruence for 6F5: an Apéry-like story, arXiv:1701.04098 [math.NT], 2017.
P. Paule and C. Schneider, Computer proofs of a new family of harmonic number identities, Adv. in Appl. Math. 31 (2003), no. 2, 359-378.
PROG
(PARI) h(n) = sum(k=1, n, 1/k);
a(n, l=7) = sum(k=0, n, binomial(n, k)^l*(1-l*k*(h(k)-h(n-k))));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 14 2024
STATUS
approved