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A321431 Expansion of Product_{i>0, j>0} 1/(1 - x^(i^2 + j^2)).

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%I A321431 #21 Nov 10 2018 10:15:33
%S A321431 1,0,1,0,1,2,1,2,2,2,7,2,7,6,7,14,8,16,18,16,34,20,38,40,39,68,54,78,
%T A321431 91,84,143,116,161,184,185,270,252,312,372,372,518,494,607,704,736,
%U A321431 944,965,1130,1311,1378,1723,1784,2081,2360,2548,3048,3250,3704,4196,4544
%N A321431 Expansion of Product_{i>0, j>0} 1/(1 - x^(i^2 + j^2)).
%H A321431 Seiichi Manyama, <a href="/A321431/b321431.txt">Table of n, a(n) for n = 0..10000</a>
%F A321431 G.f.: Product_{k>0} 1/(1 - x^k)^A063725(k).
%t A321431 nmax = 100; A063725 = Rest[CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/4, {x, 0, nmax}], x]]; s = 1; Do[s *= Sum[(-1)^j*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}]; CoefficientList[Series[1/s, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 09 2018 *)
%Y A321431 Convolution inverse of A321430.
%Y A321431 Cf. A063725, A321428, A321433, A321437.
%K A321431 nonn
%O A321431 0,6
%A A321431 _Seiichi Manyama_, Nov 09 2018