A028710 Expansion of (theta_3(z)*theta_3(5z)*theta_3(25z)+theta_2(z)*theta_2(5z)*theta_2(25z)).

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, 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, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 2

Offset

0,5

Links

Table of n, a(n) for n=0..80.

Example

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 + ...

Mathematica

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 *)

Prog

(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 */

Crossrefs

Cf. A028711, A028712, A028713.

Sequence in context: A028653 A051584 A028645 * A178926 A028637 A070208

Adjacent sequences: A028707 A028708 A028709 * A028711 A028712 A028713

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved