OFFSET
0,2
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 q^(-1/3) * eta(q)^5 * eta(q^6)^2 / (eta(q^2)^3 * eta(q^3)) in powers of q.
Euler transform of period 6 sequence [ -5, -2, -4, -2, -5, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 73728^(1/2) (t / i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227595.
-2 * a(n) = A224822(3*n + 1).
EXAMPLE
1 - 5*x + 8*x^2 - 4*x^3 + 4*x^4 - 13*x^5 + 12*x^6 - 4*x^7 + 5*x^8 - 16*x^9 + ...
q - 5*q^4 + 8*q^7 - 4*q^10 + 4*q^13 - 13*q^16 + 12*q^19 - 4*q^22 + 5*q^25 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(-1/3)* eta[q]^5*eta[q^6]^2/(eta[q^2]^3*eta[q^3]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 19 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^5 * eta(x^6 + A)^2 / (eta(x^2 + A)^3 * eta(x^3 + A)), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 21 2013
STATUS
approved