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, -5, 109, -3317, 121501, -4954505, 216867925, -9981053045, 476860000285, -23451310381505, 1180189308268609, -60519806861966105, 3152285573768063461, -166371462775232899553, 8880340127444426907109, -478649327347386225075317

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..562

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

Cf. A000984, A005258, A183204.

Cf. A001008.

Sequence in context: A318292 A012239 A012121 * A014180 A012122 A012091

Adjacent sequences: A371879 A371880 A371881 * A371883 A371884 A371885

Keyword

sign

Author

Seiichi Manyama, Apr 14 2024

Status

approved