A014787 Expansion of Jacobi theta constant (theta_2/2)^12.

1, 12, 66, 232, 627, 1452, 2982, 5544, 9669, 16016, 25158, 38160, 56266, 80124, 111816, 153528, 205260, 270876, 353870, 452496, 574299, 724044, 895884, 1103520, 1353330, 1633500, 1966482, 2360072, 2792703, 3299340, 3892922, 4533936, 5273841, 6134448

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of ways of writing n as the sum of 12 triangular numbers from A000217.

Examples

			a(2) = (A001160(7) - A000735(3))/256 = (16808 - (-88))/256 = 66. - _Wolfdieter Lang_, Jan 13 2017
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• K. Ono, S. Robins and P. T. Wahl, On the representation of integers as sums of triangular numbers, Aequationes mathematicae, August 1995, Volume 50, Issue 1-2, pp 73-94. Case k=12, Theorem 7.

Crossrefs

Column k=12 of A286180.

Cf. A000217, A000735, A001160.

Number of ways of writing n as a sum of k triangular numbers, for k=1,...: A010054, A008441, A008443, A008438, A008439, A008440, A226252, A007331, A226253, A226254, A226255, A014787, A014809.

Formula

From Wolfdieter Lang, Jan 13 2017: (Start)

G.f.: 12th power of g.f. for A010054.

a(n) = (A001160(2*n+3) - A000735(n+1))/256. See the Ono et al. link, case k=12, Theorem 7. (End)

a(0) = 1, a(n) = (12/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017

G.f.: exp(Sum_{k>=1} 12*(x^k/k)/(1 + x^k)). - Ilya Gutkovskiy, Jul 31 2017

Extensions

More terms from Seiichi Manyama, May 05 2017