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%I #26 Apr 14 2024 13:46:34
%S 1,-5,109,-3317,121501,-4954505,216867925,-9981053045,476860000285,
%T -23451310381505,1180189308268609,-60519806861966105,
%U 3152285573768063461,-166371462775232899553,8880340127444426907109,-478649327347386225075317
%N 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.
%H Seiichi Manyama, <a href="/A371882/b371882.txt">Table of n, a(n) for n = 0..562</a>
%H Robert Osburn, Armin Straub, and Wadim Zudilin, <a href="https://arxiv.org/abs/1701.04098">A modular supercongruence for 6F5: an Apéry-like story</a>, arXiv:1701.04098 [math.NT], 2017.
%H P. Paule and C. Schneider, <a href="https://doi.org/10.1016/S0196-8858(03)00016-2">Computer proofs of a new family of harmonic number identities</a>, Adv. in Appl. Math. 31 (2003), no. 2, 359-378.
%o (PARI) h(n) = sum(k=1, n, 1/k);
%o a(n, l=7) = sum(k=0, n, binomial(n, k)^l*(1-l*k*(h(k)-h(n-k))));
%Y Cf. A000984, A005258, A183204.
%Y Cf. A001008.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 14 2024