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%I #15 Oct 01 2017 09:18:29
%S 1,2,4,8,16,31,58,105,184,314,523,853,1365,2149,3332,5097,7701,11505,
%T 17009,24907,36147,52027,74304,105352,148355,207575,288673,399157,
%U 548926,750996,1022400,1385374,1868813,2510181,3357862,4474187,5939186
%N Partial sums of A001523.
%C The subsequence of primes begins: 2, 31, 523, 853, 24907, 52027, 1868813, ...
%H Alois P. Heinz, <a href="/A174439/b174439.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = Sum_{i=0..n} A001523(i).
%F a(n) ~ exp(2*Pi*sqrt(n/3))/(8*Pi*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Dec 13 2015
%t nmax = 41; A001523 = CoefficientList[Series[1 + Sum[(-1)^(k + 1)*x^(k*(k + 1)/2), {k, 1, nmax}] / QPochhammer[x]^2, {x, 0, nmax}], x]; s = 0; Table[s = s + A001523[[k]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Dec 13 2015 *)
%Y Cf. A001523, A054250, A059618, A059623, A001522, A001524, A000569, A100505, A100506.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Mar 19 2010