A335091 a(n) = ((2*n+1)!!)^3 * (Sum_{k=1..n} 1/(2*k+1)^3).

0, 1, 152, 55511, 41625144, 56246975289, 124697847089808, 423322997436687375, 2088114588247920714000, 14363296872939657999716625, 133299155158711610547152961000, 1624450039177408057102079622846375, 25413656551949715361011431877529125000, 500711137690193661025654228810320074015625

Offset: 0

Author

Seiichi Manyama, Sep 11 2020

Keywords

• nonn

Crossrefs

Column k=3 of A335095.

Cf. A271636, A291585, A334670, A335090, A335092.

Programs

Mathematica

a[n_] := ((2*n + 1)!!)^3 * Sum[1/(2*k + 1)^3, {k, 1, n}]; Array[a, 14, 0] (* Amiram Eldar, Apr 29 2021 *)

PARI

{a(n) = prod(k=1, n, 2*k+1)^3*sum(k=1, n, 1/(2*k+1)^3)}

PARI

{a(n) = if(n<2, n, ((2*n-1)^3+(2*n+1)^3)*a(n-1)-(2*n-1)^6*a(n-2))}

Formula

a(n) = ((2*n-1)^3+(2*n+1)^3) * a(n-1) - (2*n-1)^6 * a(n-2) for n>1.

a(n) ~ (7*zeta(3)/8 - 1) * 2^(3*n + 9/2) * n^(3*n + 3) / exp(3*n). - Vaclav Kotesovec, Sep 25 2020