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

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, 91, 84, 143, 116, 161, 184, 185, 270, 252, 312, 372, 372, 518, 494, 607, 704, 736, 944, 965, 1130, 1311, 1378, 1723, 1784, 2081, 2360, 2548, 3048, 3250, 3704, 4196, 4544

Offset: 0

Author

Seiichi Manyama, Nov 09 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Convolution inverse of A321430.

Cf. A063725, A321428, A321433, A321437.

Programs

Mathematica

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 *)

Formula

G.f.: Product_{k>0} 1/(1 - x^k)^A063725(k).