OFFSET
1,3
COMMENTS
Here eta(q) is the Dedekind eta function without the q^(1/24) factor (A010815).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..500
FORMULA
G.f. satisfies: eta(x/(A(x)-1)) = 1 + x.
G.f. satisfies: A(eta(x)-1) = 1 + (eta(x)-1)/x.
a(n) ~ c * d^n / n^(3/2), where d = 4.37926411884088478340484205014088510... and c = 0.13031461371242728737549949707031... - Vaclav Kotesovec, Nov 11 2017
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 6*x^4 + 19*x^5 + 64*x^6 +...
eta(x)-1 = -x - x^2 + x^5 + x^7 - x^12 - x^15 + x^22 + x^26 +...
x/(A(x)-1) = -x - x^2 - 2*x^3 - 5*x^4 - 15*x^5 - 49*x^6 - 169*x^7 -... (cf. A176025).
MATHEMATICA
Rest[CoefficientList[1 + x/InverseSeries[Series[QPochhammer[x] - 1, {x, 0, 30}]], x]] (* Vaclav Kotesovec, Nov 11 2017 *)
PROG
(PARI) {a(n)=polcoeff(1+x/serreverse(eta(x+x^2*O(x^n))-1), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 29 2010
STATUS
approved