A298330 Number of ordered ways of writing n^2 as a sum of n squares of positive integers.

1, 1, 0, 3, 1, 5, 141, 742, 6120, 43888, 300232, 3074478, 28901797, 290411147, 3175037698, 34951274416, 399750066121, 4814421349467, 59532792202344, 768079420764884, 10247011240209066, 140144002390928732, 1978092111496441512, 28633995987157024399

Offset: 0

Author

Ilya Gutkovskiy, Jan 17 2018

Keywords

• nonn

Examples

			a(3) = 3 because we have [4, 4, 1], [4, 1, 4] and [1, 4, 4].
		

Links

• Robert Israel, Table of n, a(n) for n = 0..100
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A037444, A066535, A232173, A287617, A298329.

Programs

Maple

G:= (JacobiTheta3(0,x)-1)/2:
f:= proc(n) local S; S:= series(G^n,x,n^2+1); coeff(S,x,n^2) end proc:
map(f, [$0..25]); # Robert Israel, Dec 16 2024

Mathematica

Table[SeriesCoefficient[(-1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^2}], {n, 0, 23}]

Formula

a(n) = [x^(n^2)] (Sum_{k>=1} x^(k^2))^n.