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 eta(q^2)^5 * eta(q^3)^4 * eta(q^12)^4 * eta(q^18)^5 / (eta(q)^2 * eta(q^4)^2 * eta(q^6)^10 * eta(q^9)^2 * eta(q^36)^2) in powers of q.
Euler transform of period 36 sequence [ 2, -3, -2, -1, 2, 3, 2, -1, 0, -3, 2, 1, 2, -3, -2, -1, 2, 0, 2, -1, -2, -3, 2, 1, 2, -3, 0, -1, 2, 3, 2, -1, -2, -3, 2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 Pi i t).
a(n) = 2 * A233670(n) unless n=0.
EXAMPLE
G.f. = 1 + 2*q - 4*q^3 - 6*q^4 + 12*q^6 + 16*q^7 - 28*q^9 - 36*q^10 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^9] / EllipticTheta[ 3, 0, q^3]^2, {q, 0, n}]; (* Michael Somos, Aug 27 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A)^4 * eta(x^12 + A)^4 * eta(x^18 + A)^5 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A)^10 * eta(x^9 + A)^2 * eta(x^36 + A)^2), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Dec 14 2013
STATUS
approved