A218680 O.g.f.: A(x) = Sum_{n>=0} n^n*x^n/(1-n*x)^(2*n)/n! * exp(-n*x/(1-n*x)^2).

1, 1, 3, 16, 111, 911, 8622, 91414, 1067579, 13564195, 185687381, 2718184470, 42288343176, 695667651368, 12049465530936, 218945489692574, 4160440403683643, 82448824370010887, 1699889286488298603, 36384381642357676480, 806926050321577391347, 18510872795071148287531

Offset: 0

Author

Paul D. Hanna, Nov 06 2012

Keywords

• nonn

Examples

			O.g.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 111*x^4 + 911*x^5 + 8622*x^6 +...
where
A(x) = 1 + x/(1-x)^2*exp(-x/(1-x)^2) + 2^2*x^2/(1-2*x)^4/2!*exp(-2*x/(1-2*x)^2) + 3^3*x^3/(1-3*x)^6/3!*exp(-3*x/(1-3*x)^2) + 4^4*x^4/(1-4*x)^8/4!*exp(-4*x/(1-4*x)^2) + 5^5*x^5/(1-5*x)^10/5!*exp(-5*x/(1-5*x)^2) +...
simplifies to a power series in x with integer coefficients.
		

Crossrefs

Cf. A134055.

Programs

PARI

{a(n)=local(A=1+x);A=sum(k=0,n,k^k/(1-k*x)^(2*k)*x^k/k!*exp(-k*x/(1-k*x)^2+x*O(x^n)));polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))