A291586 a(n) = ((2n-1)!!)^4 * Sum_{i=1..n} 1/(2*i-1)^4.

0, 1, 82, 51331, 123296356, 809068942341, 11846375878465206, 338356017569383549191, 17129606870671774862445000, 1430698777932227525446706735625, 186451505481090040331197201556276250, 36261458995575361475673937929555130516875

Offset: 0

Author

Seiichi Manyama, Aug 27 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..126

Crossrefs

Cf. A001147, A203229.

Programs

Mathematica

Table[(2*n-1)!!^4 * Sum[1/(2*i-1)^4, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)

Formula

a(0) = 0, a(1) = 1, a(n+1) = ((2*n-1)^4+(2*n+1)^4)*a(n) - (2*n-1)^8*a(n-1) for n > 0.

a(n) ~ Pi^4 * 2^(4*n-3) * n^(4*n) / (3*exp(4*n)). - Vaclav Kotesovec, Aug 27 2017