A291585 a(n) = ((2n-1)!!)^3 * Sum_{i=1..n} 1/(2*i-1)^3.

0, 1, 28, 3527, 1213136, 885533769, 1179489355164, 2592461355675183, 8752024838912328000, 43007026735417743104625, 295026115290377469777013500, 2732517516522603185416699320375, 33249139841891876848539850177362000, 519549434719363290227226596791835765625

Offset: 0

Author

Seiichi Manyama, Aug 27 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..160

Crossrefs

Cf. A001147, A066989.

Programs

Mathematica

Table[(2*n-1)!!^3 * Sum[1/(2*i-1)^3, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)

Formula

a(0) = 0, a(1) = 1, a(n+1) = ((2*n-1)^3+(2*n+1)^3)*a(n) - (2*n-1)^6*a(n-1) for n > 0.

a(n) ~ 7*Zeta(3) * 2^(3*n-3/2) * n^(3*n) / exp(3*n). - Vaclav Kotesovec, Aug 27 2017

a(1) = 1, a(n) = a(n-1)*(2n-1)^3 + ((2n-1)!!)^3/(2n-1)^3, for n > 1. - Daniel Suteu, Nov 01 2017