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

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%I A014805 #36 Jun 04 2017 02:41:54
%S A014805 1,16,120,576,2060,6048,15424,35200,73518,143280,263584,461376,775160,
%T A014805 1256928,1973760,3017088,4503557,6572880,9411984,13249280,18340932,
%U A014805 25034976,33739520,44879616,59057510,76949920,99212352,126838080,160884264,202296960,252645376
%N A014805 Expansion of Jacobi theta constant (theta_2/2)^16.
%C A014805 Number of ways of writing n as the sum of 16 triangular numbers from A000217. - _Seiichi Manyama_, May 05 2017
%H A014805 Seiichi Manyama, <a href="/A014805/b014805.txt">Table of n, a(n) for n = 0..10000</a>
%H A014805 J. G. Huard and K. S. Williams, <a href="https://doi.org/10.1216/rmjm/1181069710">Sums of sixteen and twenty-four triangular numbers</a>, Rocky Mountain J. Math. Volume 35, Number 3 (2005), 857-868.
%F A014805 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
%F A014805 a(0) = 1, a(n) = (16/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - _Seiichi Manyama_, May 06 2017
%Y A014805 Column k=16 of A286180.
%K A014805 nonn,easy
%O A014805 0,2
%A A014805 _N. J. A. Sloane_
%E A014805 More terms from _Seiichi Manyama_, May 05 2017