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A301466 a(n) = Sum_{k>=0} binomial(k^3, n)/2^(k+1). 3
1, 13, 2335, 1178873, 1168712311, 1916687692685, 4697337224419543, 16082097033630615185, 73313708225823014181097, 429319086610079876821621425, 3140585308524019620784003889263, 28066697522114849327295724261347841, 300886927215791917153044786581553617063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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).

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}]

CROSSREFS

Cf. A173217, A301310, A301432, A301468.

Sequence in context: A202517 A221901 A096721 * A229267 A283099 A195537

Adjacent sequences:  A301463 A301464 A301465 * A301467 A301468 A301469

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 21 2018

STATUS

approved

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Last modified January 26 09:38 EST 2021. Contains 340435 sequences. (Running on oeis4.)