A279227 - OEIS

%I #6 Dec 29 2016 17:17:44

%S 1,4,8,12,20,36,56,76,104,152,216,284,364,484,648,828,1028,1300,1664,

%T 2076,2532,3108,3848,4700,5640,6776,8200,9848,11660,13796,16424,19452,

%U 22776,26612,31240,36572,42440,49092,56968,66044,76040,87236,100280,115244

%N Expansion of Product_{k>=1} (1 + x^(k^2))^2/(1 - x^(k^2))^2.

%H Vaclav Kotesovec, <a href="/A279227/b279227.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (4-sqrt(2)) * Zeta(3/2) * exp(3 * Pi^(1/3) * ((4-sqrt(2)) * Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) / (32 * sqrt(3) * Pi^2 * n^(3/2)). - _Vaclav Kotesovec_, Dec 29 2016

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(k^2))^2/(1 - x^(k^2))^2, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A001156, A033461, A103265, A279225, A279226.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 08 2016