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Expansion of Product_{k=1..24} theta_3(q^k), where theta_3() is the Jacobi theta function.
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%I #18 Feb 16 2025 08:33:56

%S 1,2,2,6,8,10,22,26,36,60,78,106,152,202,258,370,478,602,828,1042,

%T 1332,1758,2198,2758,3572,4446,5512,7002,8614,10616,13292,16260,19792,

%U 24496,29724,35976,44062,52992,63780,77296,92518,110532,132848,158036,187674,224066,264960

%N Expansion of Product_{k=1..24} theta_3(q^k), where theta_3() is the Jacobi theta function.

%C Also the number of integer solutions (a_1, a_2, ... , a_24) to the equation a_1^2 + 2*a_2^2 + ... + 24*a_24^2 = n.

%C a(24045) = 45676735553670596752038069309732400 and a(24046) = 45676724028345437854371347712212432. So a(24045) > a(24046).

%H Seiichi Manyama, <a href="/A320248/b320248.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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), A320247 (m=16), this sequence (m=24).

%Y Cf. A320067.

%K nonn,changed

%O 0,2

%A _Seiichi Manyama_, Oct 08 2018