A321428 Expansion of Product_{i>0, j>0} (1 + x^(i^2 + j^2)).

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, 18, 28, 38, 19, 52, 34, 46, 60, 40, 78, 58, 76, 94, 75, 120, 93, 124, 140, 126, 183, 150, 200, 210, 204, 276, 239, 308, 319, 316, 417, 366, 465, 480, 484, 620, 554

Offset

0,6

Links

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

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A063725, A321380, A321429.

Sequence in context: A372876 A157030 A080844 * A362615 A362614 A336167

Adjacent sequences: A321425 A321426 A321427 * A321429 A321430 A321431

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2018

Status

approved