A279225 - OEIS

%I #12 Jan 24 2018 07:56:03

%S 1,2,3,4,7,10,13,16,22,30,38,46,58,74,90,106,129,158,190,222,264,314,

%T 370,426,495,580,674,772,886,1024,1174,1332,1512,1724,1961,2210,2494,

%U 2818,3180,3558,3984,4468,5003,5572,6202,6918,7698,8530,9440,10466,11589

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

%C Number of partitions of n into squares of 2 kinds. - _Ilya Gutkovskiy_, Jan 23 2018

%H Vaclav Kotesovec, <a href="/A279225/b279225.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 2^(2/3)) * Zeta(3/2) / (8 * sqrt(3) * Pi^2 * n^(3/2)). - _Vaclav Kotesovec_, Dec 29 2016

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

%Y Cf. A001156, A103265, A279226, A279227.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 08 2016