A335092 a(n) = ((2*n+1)!!)^4 * (Sum_{k=1..n} 1/(2*k+1)^4).

0, 1, 706, 1745731, 11575291716, 170271339664581, 4874795836698898566, 247120020454614424554375, 20656593715240068513643845000, 2693397991748017956223512587135625, 523998492940635622166679925147692626250

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = ((2*n-1)^4+(2*n+1)^4) * a(n-1) - (2*n-1)^8 * a(n-2) for n>1.

a(n) ~ (Pi^4/96 - 1) * 2^(4*n + 6) * n^(4*n + 4) / exp(4*n). - Vaclav Kotesovec, Sep 25 2020

Mathematica

a[n_] := ((2*n + 1)!!)^4 * Sum[1/(2*k + 1)^4, {k, 1, n}]; Array[a, 11, 0] (* Amiram Eldar, Apr 28 2021 *)

Prog

(PARI) {a(n) = prod(k=1, n, 2*k+1)^4*sum(k=1, n, 1/(2*k+1)^4)}
(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))}

Crossrefs

Column k=4 of A335095.

Cf. A291586, A334670, A335090, A335091.

Sequence in context: A126830 A005845 A183795 * A252692 A074869 A212476

Adjacent sequences: A335089 A335090 A335091 * A335093 A335094 A335095

Keyword

nonn

Author

Seiichi Manyama, Sep 12 2020

Status

approved