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 A028718 Expansion of (theta_3(z)*theta_3(7z)*theta_3(49z)+theta_2(z)*theta_2(7z)*theta_2(49z)). 1

%I

%S 1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,4,0,

%T 0,0,2,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,6,8,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0

%N Expansion of (theta_3(z)*theta_3(7z)*theta_3(49z)+theta_2(z)*theta_2(7z)*theta_2(49z)).

%H Antti Karttunen, <a href="/A028718/b028718.txt">Table of n, a(n) for n = 0..11958</a>

%e G.f. = 1 + 2*q^4 + 2*q^16 + 2*q^28 + 4*q^32 + 2*q^36 + 4*q^44 + 8*q^57 + 6*q^64 + 8*q^65 + ... - _Michael Somos_, Nov 23 2017

%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^4] EllipticTheta[ 3, 0, q^28] EllipticTheta[ 3, 0, q^196] + EllipticTheta[ 2, 0, q^4] EllipticTheta[ 2, 0, q^28] EllipticTheta[ 2, 0, q^196], {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^56 + A) * eta(x^392 + A))^5 / (eta(x^4 + A) * eta(x^16 + A) * eta(x^28 + A) * eta(x^112 + A) * eta(x^196 + A) * eta(x^784 + A))^2 + 8 * x^57 * (eta(x^16 + A) * eta(x^112 + A) * eta(x^784 + A))^2 / (eta(x^8 + A) * eta(x^56 + A) * eta(x^392 + A)), n))}; /* _Michael Somos_, Nov 23 2017 */

%Y Cf. A028719, A028720, A028721.

%K nonn

%O 0,5

%A _N. J. A. Sloane_

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Last modified November 26 10:15 EST 2022. Contains 358356 sequences. (Running on oeis4.)