A280225 - OEIS

%I #5 Dec 29 2016 11:08:38

%S 1,4,5,9,17,34,47,75,109,165,240,341,473,671,936,1268,1722,2325,3091,

%T 4099,5403,7083,9207,11923,15339,19682,25134,31909,40378,50954,64068,

%U 80171,100089,124506,154465,191043,235636,289816,355673,435285,531486,647478

%N G.f.: Product_{k>=1} (1 + 3*x^(k^2)) / (1-x^k).

%C Convolution of A279368 and A000041.

%C In general, if m >= 0 and g.f. = Product_{k>=1} (1 + m*x^(k^2)) / (1-x^k), then a(n) ~ exp(Pi*sqrt((2*n)/3) + 3^(1/4)*c*n^(1/4)/ 2^(3/4) - 3*c^2/(32*Pi)) / (4*sqrt(3)*sqrt(m+1)*n), where c = -PolyLog(3/2, -m).

%H Vaclav Kotesovec, <a href="/A280225/b280225.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt((2*n)/3) + 3^(1/4)*c*n^(1/4)/ 2^(3/4) - 3*c^2/(32*Pi)) / (8*sqrt(3)*n), where c = -PolyLog(3/2, -3).

%t nmax=50; CoefficientList[Series[Product[(1+3*x^(k^2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000041, A033461, A279368, A280204, A280224.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 29 2016