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^(-1/8) * eta(q^4)^10 / (eta(q) * eta(q^2)^2 * eta(q^8)^4) in powers of q.
Euler transform of period 8 sequence [ 1, 3, 1, -7, 1, 3, 1, -3, ...].
a(3*n + 2) = 4 * A213023(n).
EXAMPLE
G.f. = 1 + x + 4*x^2 + 5*x^3 + 4*x^4 + 8*x^5 + x^6 + 4*x^7 + 8*x^8 + 4*x^9 + ...
G.f. = q + q^9 + 4*q^17 + 5*q^25 + 4*q^33 + 8*q^41 + q^49 + 4*q^57 + 8*q^65 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q^4]^10 / (QPochhammer[ q] QPochhammer[ q^2]^2 QPochhammer[ q^8]^4), {q, 0, n}]
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^10 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^4), n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 27 2013
STATUS
approved