A352471 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1)^3 * a(n-2*k-1).

1, 1, 8, 217, 13952, 1752001, 380168432, 130996038265, 67377689108480, 49343690620021249, 49570079811804165008, 66280482720537078211945, 115058150837606807142692096, 253942526419333142443328522689, 700015299612132412448976873339008

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2022

Keywords

• nonn

Crossrefs

Cf. A006154, A336195, A352468, A352470.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 2 k + 1]^3 a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[1/(1 - Sum[x^(2 k + 1)/(2 k + 1)!^3, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3

Formula

Sum_{n>=0} a(n) * x^n / n!^3 = 1 / (1 - Sum_{n>=0} x^(2*n+1) / (2*n+1)!^3).