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%I #8 Nov 23 2017 21:33:30
%S 1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0,4,0,0,0,0,0,0,8,0,0,
%T 0,0,6,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,4,0,0,0,0,0,0,0,2,0,0,0,
%U 0,0,0,8,0,0,0,0,0,0,0,16,2
%N Expansion of (theta_3(z)*theta_3(5z)*theta_3(25z)+theta_2(z)*theta_2(5z)*theta_2(25z)).
%e G.f. = 1 + 2*q^4 + 2*q^16 + 2*q^20 + 4*q^24 + 8*q^31 + 6*q^36 + 8*q^39 + 8*q^55 + 4*q^56 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^4] EllipticTheta[ 3, 0, q^20] EllipticTheta[ 3, 0, q^100] + EllipticTheta[ 2, 0, q^4] EllipticTheta[ 2, 0, q^20] EllipticTheta[ 2, 0, q^100], {q, 0, n}]; (* _Michael Somos_, Nov 23 2017 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^8 + A) * eta(x^40 + A) * eta(x^200 + A))^5 / (eta(x^4 + A) * eta(x^16 + A) * eta(x^20 + A) * eta(x^80 + A) * eta(x^100 + A) * eta(x^400 + A))^2 + 8 * x^31 * (eta(x^16 + A) * eta(x^80 + A) * eta(x^400 + A))^2 / (eta(x^8 + A) * eta(x^40 + A) * eta(x^200 + A)), n))}; /* _Michael Somos_, Nov 23 2017 */
%Y Cf. A028711, A028712, A028713.
%K nonn
%O 0,5
%A _N. J. A. Sloane_.