OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of phi(x^3) * f(x, x^5)^2 in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of phi(x) * c(x^2) / 3 in powers of x where phi() is a Ramanujan theta function and c() is a cubic AGM theta function.
Expansion of q^(-2/3) * eta(q^2)^4 * eta(q^6)^3 / (eta(q)^2 * eta(q^4)^2) in powers of q.
Euler transform of period 12 sequence [ 2, -2, 2, 0, 2, -5, 2, 0, 2, -2, 2, -3, ...].
EXAMPLE
G.f. = 1 + 2*x + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 2*x^6 + 6*x^8 + 6*x^9 + ...
G.f. = q^2 + 2*q^5 + q^8 + 2*q^11 + 4*q^14 + 4*q^17 + 2*q^20 + 6*q^26 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2]^2 QPochhammer[ x^6]^3, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^6 + A)^3 / (eta(x + A)^2 * eta(x^4 + A)^2), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 25 2015
STATUS
approved