OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of phi(-q)^2 * phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
Expansion of eta(q)^4 * eta(q^3)^2 / (eta(q^2)^2 * eta(q^6)) in powers of q.
G.f.: theta_4(q)^2 * theta_4(q^3) = (Sum_{k in Z} (-1)^k * x^k^2)^2 * (Sum_{k in Z} (-1)^k * x^(3*k^2)).
EXAMPLE
1 - 4*q + 4*q^2 - 2*q^3 + 12*q^4 - 16*q^5 - 8*q^7 + 20*q^8 - 4*q^9 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q]^2 EllipticTheta[ 4, 0, q^3], {q, 0 , n}]
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^3 + A)^2 / (eta(x^2 + A)^2 * eta(x^6 + A)), n))}
(PARI) q='q+O('q^99); Vec(eta(q)^4*eta(q^3)^2/(eta(q^2)^2*eta(q^6))) \\ Altug Alkan, Apr 12 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 20 2013
STATUS
approved