login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Expansion of Product_{k>=1} 1/(1 - x^(k^2))^2.
9

%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