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%I #10 Oct 08 2018 08:45:36
%S 1,2,2,6,8,10,22,26,36,60,78,106,152,200,252,360,456,564,770,940,1178,
%T 1532,1852,2256,2858,3430,4100,5086,5982,7076,8612,10040,11672,13960,
%U 16068,18496,21866,24796,28288,32924,37074,41876,48156,53732,60014,68546,75836,83996
%N Expansion of Product_{k=1..12} theta_3(q^k), where theta_3() is the Jacobi theta function.
%C Also the number of integer solutions (a_1, a_2, ... , a_12) to the equation a_1^2 + 2*a_2^2 + ... + 12*a_12^2 = n.
%H Seiichi Manyama, <a href="/A320246/b320246.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%Y Product_{k=1..m} theta_3(q^k): A000122 (m=1), A033715 (m=2), A029594 (m=3), A320139 (m=4), A320231 (m=5), A320232 (m=6), A320233 (m=7), A320234 (m=8), A320241 (m=9), A320242 (m=10), this sequence (m=12), A320247 (m=16).
%Y Cf. A320067.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 08 2018
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