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 f(x) * f(-x^2) * f(-x^6) / f(x^3)^3 in powers of x where f() is a Ramanujan theta function.
Euler transform of period 12 sequence [ 1, -3, -2, -2, 1, 2, 1, -2, -2, -3, 1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 3 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A261325.
EXAMPLE
G.f. = 1 + x - 2*x^2 - 4*x^3 - 3*x^4 + 4*x^5 + 12*x^6 + 8*x^7 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x] QPochhammer[ x^2] QPochhammer[ x^6] / QPochhammer[ -x^3]^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^3 + A)^3 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^8), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 14 2015
STATUS
approved