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%I #22 Apr 28 2021 02:03:15
%S 0,1,706,1745731,11575291716,170271339664581,4874795836698898566,
%T 247120020454614424554375,20656593715240068513643845000,
%U 2693397991748017956223512587135625,523998492940635622166679925147692626250
%N a(n) = ((2*n+1)!!)^4 * (Sum_{k=1..n} 1/(2*k+1)^4).
%F a(n) = ((2*n-1)^4+(2*n+1)^4) * a(n-1) - (2*n-1)^8 * a(n-2) for n>1.
%F a(n) ~ (Pi^4/96 - 1) * 2^(4*n + 6) * n^(4*n + 4) / exp(4*n). - _Vaclav Kotesovec_, Sep 25 2020
%t a[n_] := ((2*n + 1)!!)^4 * Sum[1/(2*k + 1)^4, {k, 1, n}]; Array[a, 11, 0] (* _Amiram Eldar_, Apr 28 2021 *)
%o (PARI) {a(n) = prod(k=1, n, 2*k+1)^4*sum(k=1, n, 1/(2*k+1)^4)}
%o (PARI) {a(n) = if(n<2, n, ((2*n-1)^4+(2*n+1)^4)*a(n-1)-(2*n-1)^8*a(n-2))}
%Y Column k=4 of A335095.
%Y Cf. A291586, A334670, A335090, A335091.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 12 2020
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