A014805 Expansion of Jacobi theta constant (theta_2/2)^16.

1, 16, 120, 576, 2060, 6048, 15424, 35200, 73518, 143280, 263584, 461376, 775160, 1256928, 1973760, 3017088, 4503557, 6572880, 9411984, 13249280, 18340932, 25034976, 33739520, 44879616, 59057510, 76949920, 99212352, 126838080, 160884264, 202296960, 252645376

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of ways of writing n as the sum of 16 triangular numbers from A000217. - Seiichi Manyama, May 05 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• J. G. Huard and K. S. Williams, Sums of sixteen and twenty-four triangular numbers, Rocky Mountain J. Math. Volume 35, Number 3 (2005), 857-868.

Crossrefs

Column k=16 of A286180.

Formula

a(n) = 1/192 * Sum_{a, b, x, y > 0, a*x + b*y = 2*n + 4, a == b == x == y == 1 mod 2 and a > b} a*b*(a^2 - b^2)^2. - Seiichi Manyama, May 05 2017

a(0) = 1, a(n) = (16/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017

Extensions

More terms from Seiichi Manyama, May 05 2017