A260671 Expansion of theta_3(q) * theta_3(q^15) in powers of q.
1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 10, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0
Offset: 0
Keywords
Examples
G.f. = 1 + 2*x + 2*x^4 + 2*x^9 + 2*x^15 + 6*x^16 + 4*x^19 + 4*x^24 + 2*x^25 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
Programs
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Mathematica
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^15], {q, 0, n}]; -
PARI
{a(n) = if( n<1, n==0, qfrep([1, 0; 0, 15], n)[n]*2)}; -
PARI
{a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^30 + A))^5 / (eta(x + A) * eta(x^4 + A) * eta(x^15 + A) * eta(x^60 + A))^2, n))}; -
PARI
q='q+O('q^99); Vec((eta(q^2)*eta(q^30))^5/(eta(q)*eta(q^4)*eta(q^15)*eta(q^60))^2) \\ Altug Alkan, Jul 18 2018
Formula
Expansion of (eta(q^2) * eta(q^30))^5 / (eta(q) * eta(q^4) * eta(q^15) * eta(q^60))^2 in powers of q.
Euler transform of a period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = 60^(1/2) (t/i) f(t) where q = exp(2 Pi i t).
G.f.: (Sum_{k in Z} x^(k^2)) * (Sum_{k in Z} x^(15*k^2)).
a(3*n + 2) = a(4*n + 2) = a(5*n + 2) = a(5*n + 3) = 0.
a(5*n) = A192323(n).
Comments