A217906 O.g.f.: 1 / Sum_{n>=0} -n^n*(n-1)^(n-1) * exp(-n*(n-1)*x) * x^n / n!.

1, 1, 3, 19, 223, 4019, 98071, 3012595, 111408735, 4813926235, 237893755847, 13230156372931, 817650834368367, 55588558619887179, 4122802071853330711, 331247290236326404499, 28660436738240190615167, 2656810905539387715877787, 262694577305483845458361767

Offset: 0

Author

Paul D. Hanna, Oct 14 2012

Keywords

• nonn

Examples

			O.g.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 223*x^4 + 4019*x^5 + 98071*x^6 +...
where
A(x) = 1/(1 - 1^1*0^0*x*exp(-1*0*x) - 2^2*1^1*exp(-2*1*x)*x^2/2! - 3^3*2^2*exp(-3*2*x)*x^3/3! - 4^4*3^3*exp(-4*3*x)*x^4/4! - 5^5*4^4*exp(-5*4*x)*x^5/5! +...).
simplifies to a power series in x with integer coefficients.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A217905.

Programs

PARI

{a(n)=polcoeff(1/sum(m=0,n,-m^m*(m-1)^(m-1)*x^m*exp(-m*(m-1)*x+x*O(x^n))/m!),n)}
for(n=0,30,print1(a(n),", "))

Formula

Convolution inverse of A217905.

a(n) ~ 2^(2*n - 2) * n^(n - 3/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^(n - 1/2) * (2-c)^(n-1)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Aug 22 2018