OFFSET
3,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..2500
FORMULA
Expansion of b(q) * c(q) * b(q^8) * c(q^8) / 9 in powers of q where b(), c() are cubic AGM theta functions.
Euler transform of period 24 sequence [ -2, -2, -4, -2, -2, -4, -2, -4, -4, -2, -2, -4, -2, -2, -4, -4, -2, -4, -2, -2, -4, -2, -2, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 576 (t/i)^4 f(t) where q = exp(2 Pi i t).
G.f.: x^3 * (Product_{k>0} (1 - x^k) * (1 - x^(3*k)) * (1 - x^(8*k)) * (1 - x^(24*k)))^2.
a(4*n) = -2 * A030209(n). a(4*n + 2) = 0.
EXAMPLE
x^3 - 2*x^4 - x^5 + 5*x^7 + 4*x^8 - 7*x^9 - 7*x^11 + 6*x^12 - 2*x^13 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]* eta[q^3]*eta[q^8]*eta[q^24])^2, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<3, 0, n = n-3; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^3 + A) * eta(x^8 + A) * eta(x^24 + A))^2, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 26 2012
STATUS
approved