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%I #10 Mar 22 2018 12:16:39
%S 1,13,2335,1178873,1168712311,1916687692685,4697337224419543,
%T 16082097033630615185,73313708225823014181097,
%U 429319086610079876821621425,3140585308524019620784003889263,28066697522114849327295724261347841,300886927215791917153044786581553617063
%N a(n) = Sum_{k>=0} binomial(k^3, n)/2^(k+1).
%H Vaclav Kotesovec, <a href="/A301466/b301466.txt">Table of n, a(n) for n = 0..175</a>
%F a(n) ~ 3^(3*n + 1/2) * n^(2*n) / (2 * exp(2*n) * (log(2))^(3*n + 1)).
%F G.f.: Sum_{n>=0} (1 + x)^(n^3) / 2^(n+1).
%t Table[Sum[Binomial[k^3, n]/2^(k+1), {k, 0, Infinity}], {n, 0, 15}]
%t Table[Sum[StirlingS1[n, j] * HurwitzLerchPhi[1/2, -3*j, 0]/2, {j, 0, n}] / n!, {n, 0, 15}]
%Y Cf. A173217, A301310, A301432, A301468.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 21 2018
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