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^(-17/24) * eta(q^3)^2 * eta(q^6)^2 / eta(q) in powers of q.
Euler transform of period 6 sequence [ 1, 1, -1, 1, 1, -3, ...].
G.f.: Product_{k>0} (1 - x^(3*k))^2 * (1 - x^(6*k))^2 / (1 - x^k).
EXAMPLE
1 + x + 2*x^2 + x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 5*x^9 + ...
q^17 + q^41 + 2*q^65 + q^89 + 3*q^113 + 3*q^137 + 2*q^161 + 2*q^185 + ...
MATHEMATICA
QP := QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^3]*QP[q^6])^2/QP[q], {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)^2 * eta(x^6 + A)^2 / eta(x + A), n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 16 2012
STATUS
approved