A109747 E.g.f.: exp(-exp(-x)+1+x).

1, 2, 3, 3, 2, 3, 5, -4, 5, 55, -212, 201, 2381, -15350, 35183, 145359, -1821438, 8117231, -521487, -278996548, 2261959961, -7554900397, -34727188796, 690775844605, -4901767330647, 10921820177234, 179314430713387, -2668801066419061, 18150518618843778

Offset: 0

Author

Franklin T. Adams-Watters and Vladeta Jovovic, Aug 10 2005

Keywords

• easy
• sign

Comments

Equals double binomial transform of A014182. - Gary W. Adamson, Dec 31 2008

Examples

			G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + 3*x^5 + 5*x^6 - 4*x^7 + 5*x^8 + 55*x^9 + ...
		

Crossrefs

Cf. A080094.

Cf. A014182. - Gary W. Adamson, Dec 31 2008

Programs

Maple

G:=exp(-exp(-x)+1+x): Gser:=series(G,x=0,32): seq(n!*coeff(Gser,x,n),n=0..28); # Emeric Deutsch, Apr 10 2006

Mathematica

With[{nn=30},CoefficientList[Series[Exp[-Exp[-x]+1+x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jun 22 2018 *)

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling2(n, k)*A000522(k).

G.f. = (1 - x^2 * Sum_{k>0} k * x^k / ((1 + x) * (1 + 2*x) + ... (1 + k*x))) / (1 - x)^2. - Michael Somos, Nov 07 2014

G.f.: 1/(1-x*Q(0)), where Q(k)= 1 + x/(1 - x - x*(k+1)/(x - 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 19 2013

G.f.: 1/W(0), where W(k) = 1 - x - x/(1 + x*(k+1)/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 07 2014

a(n) = exp(1) * (-1)^n * Sum_{k>=0} (-1)^k * (k - 1)^n / k!. - Ilya Gutkovskiy, Dec 20 2019

Extensions

More terms from Emeric Deutsch, Apr 10 2006