A321430 Expansion of Product_{i>0, j>0} (1 - x^(i^2 + j^2)).

1, 0, -1, 0, 0, -2, 0, 2, -1, 0, 0, 0, 1, 0, 0, 4, 0, -6, 4, 2, -7, 2, 7, -2, -4, 2, -4, 0, 0, -4, 11, 2, -16, 2, 13, -16, 0, 22, -12, -4, 2, -14, 12, 10, -17, 20, 27, -48, -4, 34, -27, -2, 22, -6, -4, 4, -35, 32, 45, -72, 29, 66, -81, -40, 76, -28, -24, 68, -56, 28

Offset: 0

Author

Seiichi Manyama, Nov 09 2018

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A063725, A321428, A321431, A321432.

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}]; Take[CoefficientList[s, x], nmax + 1] (* Vaclav Kotesovec, Nov 09 2018 *)

Formula

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