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A320233 Expansion of Product_{k=1..7} theta_3(q^k), where theta_3() is the Jacobi theta function. 9

%I

%S 1,2,2,6,8,10,22,26,34,54,68,84,114,144,156,216,256,268,350,384,414,

%T 508,564,560,686,758,736,914,966,948,1140,1308,1182,1460,1640,1464,

%U 1928,2024,1928,2228,2564,2320,2748,3164,2584,3350,3640,3232,3738,4314,3566,4400

%N Expansion of Product_{k=1..7} theta_3(q^k), where theta_3() is the Jacobi theta function.

%C Also the number of integer solutions (a_1, a_2, ... , a_7) to the equation a_1^2 + 2*a_2^2 + ... + 7*a_7^2 = n.

%H Seiichi Manyama, <a href="/A320233/b320233.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), this sequence (m=7), A320234 (m=8).

%Y Cf. A320067.

%K nonn,look

%O 0,2

%A _Seiichi Manyama_, Oct 08 2018

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Last modified February 25 11:20 EST 2020. Contains 332233 sequences. (Running on oeis4.)