A301466 a(n) = Sum_{k>=0} binomial(k^3, n)/2^(k+1).

1, 13, 2335, 1178873, 1168712311, 1916687692685, 4697337224419543, 16082097033630615185, 73313708225823014181097, 429319086610079876821621425, 3140585308524019620784003889263, 28066697522114849327295724261347841, 300886927215791917153044786581553617063

Offset: 0

Author

Vaclav Kotesovec, Mar 21 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..175

Crossrefs

Cf. A173217, A301310, A301432, A301468.

Programs

Mathematica

Table[Sum[Binomial[k^3, n]/2^(k+1), {k, 0, Infinity}], {n, 0, 15}]
Table[Sum[StirlingS1[n, j] * HurwitzLerchPhi[1/2, -3*j, 0]/2, {j, 0, n}] / n!, {n, 0, 15}]

Formula

a(n) ~ 3^(3*n + 1/2) * n^(2*n) / (2 * exp(2*n) * (log(2))^(3*n + 1)).

G.f.: Sum_{n>=0} (1 + x)^(n^3) / 2^(n+1).