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A320247 Expansion of Product_{k=1..16} theta_3(q^k), where theta_3() is the Jacobi theta function. 4

%I

%S 1,2,2,6,8,10,22,26,36,60,78,106,152,202,258,370,478,600,822,1032,

%T 1310,1720,2140,2656,3418,4222,5172,6510,7922,9636,11928,14424,17268,

%U 21088,25236,29996,36222,42824,50544,60252,70830,82832,97732,113956,132242,154866,179164,206396

%N Expansion of Product_{k=1..16} theta_3(q^k), where theta_3() is the Jacobi theta function.

%C Also the number of integer solutions (a_1, a_2, ... , a_16) to the equation a_1^2 + 2*a_2^2 + ... + 16*a_16^2 = n.

%H Seiichi Manyama, <a href="/A320247/b320247.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), A320246 (m=12), this sequence (m=16).

%Y Cf. A320067.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 08 2018

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Last modified April 6 18:38 EDT 2020. Contains 333286 sequences. (Running on oeis4.)