OFFSET
0,3
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 q^(-1/3) * eta(q^3)^3 * eta(q^4)^5 / (eta(q) * eta(q^2)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 24 sequence [ 1, 3, -2, -2, 1, 0, 1, 0, -2, 3, 1, -5, 1, 3, -2, 0, 1, 0, 1, -2, -2, 3, 1, -3, ...].
a(16*n + 15) = 0. a(4*n + 1) = a(n).
EXAMPLE
1 + x + 4*x^2 + 2*x^3 + 6*x^4 + x^5 + 6*x^6 + 2*x^7 + 7*x^8 + 4*x^9 + ...
q + q^4 + 4*q^7 + 2*q^10 + 6*q^13 + q^16 + 6*q^19 + 2*q^22 + 7*q^25 + ...
MATHEMATICA
QP := QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^3]^3*QP[q^4]^5)/( QP[q]*QP[q^2]^2*QP[q^8]^2), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 07 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^4 + A)^5 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^2), n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 15 2012
STATUS
approved