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Expansion of (theta_3(z)*theta_3(23z) + theta_2(z)*theta_2(23z))^6.
3

%I #12 Feb 20 2020 02:17:55

%S 1,12,60,160,252,312,568,1200,2004,3036,4680,7008,10264,14568,21024,

%T 31280,42012,54408,75284,99600,129912,168688,210240,272460,336048,

%U 404052,516432,618224,736272,884712,1033008,1244976,1439820,1666800,1953288,2232000,2548516,2893848,3376224,3756912,4294344

%N Expansion of (theta_3(z)*theta_3(23z) + theta_2(z)*theta_2(23z))^6.

%H Jinyuan Wang, <a href="/A328094/b328094.txt">Table of n, a(n) for n = 0..1000</a>

%H Bülent Köklüce, <a href="https://doi.org/10.1007/s11139-013-9480-4">Cusp forms in S_6 (Gamma_ 0(23)), S_8 (Gamma_0 (23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables</a>, The Ramanujan Journal 34.2 (2014): 187-208. See F_6, p. 196.

%o (PARI) a(n) = polcoeff((1 + 2*x*Ser(qfrep([2, 1; 1, 12], n, 1)))^6, n); \\ _Jinyuan Wang_, Feb 20 2020

%Y Cf. A028959, A028659, A028660, A328093.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 17 2019