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%I #14 Nov 09 2018 10:37:23
%S 1,0,1,0,0,2,0,2,1,0,4,0,3,4,0,8,0,6,8,2,13,2,9,14,4,22,8,16,24,8,35,
%T 18,28,38,19,52,34,46,60,40,78,58,76,94,75,120,93,124,140,126,183,150,
%U 200,210,204,276,239,308,319,316,417,366,465,480,484,620,554
%N Expansion of Product_{i>0, j>0} (1 + x^(i^2 + j^2)).
%H Seiichi Manyama, <a href="/A321428/b321428.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{k>0} (1 + x^k)^A063725(k).
%t nmax = 100; A063725 = Rest[CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/4, {x, 0, nmax}], x]]; s = 1; Do[s *= Sum[Binomial[A063725[[k]], j]*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]];, {k, 2, nmax}]; Take[CoefficientList[s, x], nmax + 1] (* _Vaclav Kotesovec_, Nov 09 2018 *)
%Y Cf. A063725, A321380, A321429.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Nov 09 2018
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