login
A192323
Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.
6
1, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 6, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,4
LINKS
FORMULA
Expansion of (eta(q^6) * eta(q^10))^5 / (eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20))^2 in powers of q.
Euler transform of a period 60 sequence.
G.f.: (Sum_{k} x^(3 * k^2)) * (Sum_{k} x^(5 * k^2)).
a(3*n + 1) = a(4*n + 2) = a(5*n + 1) = a(5*n + 4) = 0. a(4*n) = A028956(n).
a(n) = A122855(n) - A140727(n). a(5*n) = A260671(n).
EXAMPLE
G.f. = 1 + 2*q^3 + 2*q^5 + 4*q^8 + 2*q^12 + 4*q^17 + 2*q^20 + 4*q^23 + 2*q^27 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] EllipticTheta[ 3, 0, q^5], {q, 0, n}];
PROG
(PARI) {a(n) = if( n<1, n==0, qfrep([3, 0; 0, 5], n)[n]*2)};
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A))^5 / (eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A))^2, n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 01 2011
STATUS
approved