A291587 a(n) = ((2n-1)!!)^5 * Sum_{i=1..n} 1/(2*i-1)^5.

0, 1, 244, 762743, 12820180976, 757031629267449, 121921454556651769524, 45268703999809586294371407, 34375967164840303438628549400000, 48808991831991566280900452880679940625, 120855944455445379138034328603009420077012500

Offset: 0

Author

Seiichi Manyama, Aug 27 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..105

Crossrefs

Cf. A001147, A099827.

Cf. A004041, A001824, A291585, A291586.

Programs

Mathematica

Table[(2*n-1)!!^5 * Sum[1/(2*i-1)^5, {i, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Aug 27 2017 *)

Formula

a(0) = 0, a(1) = 1, a(n+1) = ((2*n-1)^5+(2*n+1)^5)*a(n) - (2*n-1)^10*a(n-1) for n > 0.

a(n) ~ 31*Zeta(5) * 2^(5*n-5/2) * n^(5*n) / exp(5*n). - Vaclav Kotesovec, Aug 27 2017