OFFSET
-1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
FORMULA
Expansion of eta(q) * eta(q^2) / (eta(q^9) * eta(q^18)) in powers of q.
Euler transform of period 18 sequence [ -1, -2, -1, -2, -1, -2, -1, -2, 0, -2, -1, -2, -1, -2, -1, -2, -1, 0, ...]. - Corrected by Sean A. Irvine, Mar 06 2020
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^4 + v^4 - u*v * ((u + v)^2 + 9*(u + v) + u*v * (u + v + 4)).
EXAMPLE
G.f. = 1/q - 1 - 2*q + q^2 + 2*q^4 + q^5 - q^8 - 4*q^10 - q^11 + 4*q^13 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ q^(-1) QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^9] QPochhammer[ q^18]), {q, 0, n}] (* Michael Somos, Oct 23 2013 *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x + x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) / (eta(x^9 + A) * eta(x^18 + A)), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 17 2004
EXTENSIONS
Edited for better readability and coherence. - Michael Somos, Oct 23 2013
STATUS
approved