OFFSET
0,4
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 eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 * eta(q^18)^2 / (eta(q) * eta(q^6)^8 * eta(q^36)) in powers of q.
Euler transform of period 36 sequence [ 1, -1, -2, -1, 1, 4, 1, -1, -2, -1, 1, 1, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 1, 1, -1, -2, -1, 1, 4, 1, -1, -2, -1, 1, 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) = A233670(n) unless n=0.
EXAMPLE
G.f. = 1 + q - 2*q^3 - 3*q^4 + 6*q^6 + 8*q^7 - 14*q^9 - 18*q^10 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[eta[q^2]^2 *eta[q^3]^3*eta[q^12]^3*eta[q^18]^2/(eta[q]*eta[q^6]^8*eta[q^36]), {q, 0, 50}], q] (* G. C. Greubel, Aug 08 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 * eta(x^18 + A)^2 / (eta(x + A) * eta(x^6 + A)^8 * eta(x^36 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Dec 14 2013
STATUS
approved