OFFSET
0,3
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
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 *)
PROG
(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))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 11 2020
STATUS
approved