A176950 G.f.: A(x) = 1 + x/Series_Reversion(eta(x) - 1).

1, 1, 2, 6, 19, 64, 223, 799, 2927, 10922, 41382, 158800, 615939, 2410880, 9510650, 37774357, 150929671, 606239784, 2446566976, 9915210221, 40336587662, 164662328192, 674300310836, 2769234827610, 11402791485018, 47067085053193

Offset: 1

Author

Paul D. Hanna, Apr 29 2010

Keywords

• nonn

Comments

Here eta(q) is the Dedekind eta function without the q^(1/24) factor (A010815).

Examples

			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).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A176025.

Programs

Mathematica

Rest[CoefficientList[1 + x/InverseSeries[Series[QPochhammer[x] - 1, {x, 0, 30}]], x]] (* Vaclav Kotesovec, Nov 11 2017 *)

PARI

{a(n)=polcoeff(1+x/serreverse(eta(x+x^2*O(x^n))-1),n)}

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