OFFSET
1,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
Expansion of eta(q)/eta(q^9)*(eta(q^18)/eta(q^2))^2 in powers of q.
Euler transform of period 18 sequence [ -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, ...].
G.f.: A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v +v*(2*u -3*u^2 +v).
G.f.: x*Product_{k>0} (1-x^k)*(1-x^(18k))^2/((1-x^(2k))^2*(1-x^(9k))).
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n)/3) / (2*3^(3/2)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017
MATHEMATICA
eta[x_] := x^(1/24)*QPochhammer[x]; A124243[n_] := SeriesCoefficient[ (eta[q]/eta[q^9])*(eta[q^18]/eta[q^2])^2, {q, 0, n}]; Table[A124243[n], {n, 0, 50}] (* G. C. Greubel, Aug 26 2017 *)
PROG
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^18+A)^2/eta(x^2+A)^2/eta(x^9+A), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 28 2006
STATUS
approved