%I #7 Nov 11 2017 11:07:22
%S 1,1,2,6,19,64,223,799,2927,10922,41382,158800,615939,2410880,9510650,
%T 37774357,150929671,606239784,2446566976,9915210221,40336587662,
%U 164662328192,674300310836,2769234827610,11402791485018,47067085053193
%N G.f.: A(x) = 1 + x/Series_Reversion(eta(x) - 1).
%C Here eta(q) is the Dedekind eta function without the q^(1/24) factor (A010815).
%H Vaclav Kotesovec, <a href="/A176950/b176950.txt">Table of n, a(n) for n = 1..500</a>
%F G.f. satisfies: eta(x/(A(x)-1)) = 1 + x.
%F G.f. satisfies: A(eta(x)-1) = 1 + (eta(x)-1)/x.
%F a(n) ~ c * d^n / n^(3/2), where d = 4.37926411884088478340484205014088510... and c = 0.13031461371242728737549949707031... - _Vaclav Kotesovec_, Nov 11 2017
%e G.f.: A(x) = x + x^2 + 2*x^3 + 6*x^4 + 19*x^5 + 64*x^6 +...
%e eta(x)-1 = -x - x^2 + x^5 + x^7 - x^12 - x^15 + x^22 + x^26 +...
%e x/(A(x)-1) = -x - x^2 - 2*x^3 - 5*x^4 - 15*x^5 - 49*x^6 - 169*x^7 -... (cf. A176025).
%t Rest[CoefficientList[1 + x/InverseSeries[Series[QPochhammer[x] - 1, {x, 0, 30}]], x]] (* _Vaclav Kotesovec_, Nov 11 2017 *)
%o (PARI) {a(n)=polcoeff(1+x/serreverse(eta(x+x^2*O(x^n))-1),n)}
%Y Cf. A176025.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Apr 29 2010