OFFSET
3,5
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion (1/3) * b(q^2) * c(q^10) * (c(q) * b(q^5) / (b(q) * c(q^5)))^(1/4) in powers of q where b(), c() are cubic AGM theta functions.
Expansion of eta(q^2)^3 * eta(q^3) * eta(q^5) * eta(q^30)^3 / (eta(q) * eta(q^6) * eta(q^10) * eta(q^15)) in powers of q.
Euler transform of period 30 sequence [ 1, -2, 0, -2, 0, -2, 1, -2, 0, -2, 1, -2, 1, -2, 0, -2, 1, -2, 1, -2, 0, -2, 1, -2, 0, -2, 0, -2, 1, -4, ...].
EXAMPLE
G.f. = q^3 + q^4 - q^5 - q^6 - 2*q^7 - 2*q^8 + q^10 + 2*q^11 + 2*q^13 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[ eta[q^2]^3* eta[q^3]*eta[q^5]*eta[q^30]^3/(eta[q]*eta[q^6]*eta[q^10]*eta[q^15]), {q, 0, 60}], q]] (* G. C. Greubel, Aug 13 2018 *)
PROG
(PARI) {a(n) = my(A); n-=3; if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A) * eta(x^5 + A) * eta(x^30 + A)^3 / (eta(x + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A)), n))};
(Magma) Basis( CuspForms( Gamma0(30), 2), 89) [3];
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 26 2014
STATUS
approved