A220282 E.g.f.: 1/(1-x) = Sum_{n>=0} a(n) * exp(-n^2*x) * x^n/n!.

1, 1, 4, 51, 1480, 79765, 7010496, 920281831, 169526669824, 41844075277545, 13357347571244800, 5362349333225289691, 2646862288162043664384, 1576780272924188221429501, 1116120717235502072828661760, 926421799655193830945493519375, 891516461371835173578650979598336

Offset: 0

Author

Paul D. Hanna, Dec 11 2012

Keywords

• nonn

Comments

Compare to the identity: 1/(1-x) = Sum_{n>=0} n^n * exp(-n*x) * x^n/n!.

Compare to the o.g.f. of A007820:

Sum_{n>=0} S2(2*n,n)*x^n = Sum_{n>=0} (n^2)^n * exp(-n^2*x) * x^n/n!.

Examples

			E.g.f.: 1/(1-x) = 1 + 1*exp(-x)*x + 4*exp(-2^2*x)*x^2/2! + 51*exp(-3^2*x)*x^3/3! + 1480*exp(-4^2*x)*x^4/4! + 79765*exp(-5^2*x)*x^5/5! + 7010496*exp(-6^2*x)*x^6/6!+...
		

Crossrefs

Cf. A007820, A210029.

Programs

PARI

{a(n)=n!*polcoeff(1/(1-x+x*O(x^n))-sum(k=0,n-1,a(k)*x^k/k!*exp(-k^2*x+x*O(x^n))), n)}
for(n=0,16,print1(a(n),", "))