OFFSET
0,2
COMMENTS
Equals double binomial transform of A014182. - Gary W. Adamson, Dec 31 2008
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
EXAMPLE
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 + ...
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 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Franklin T. Adams-Watters and Vladeta Jovovic, Aug 10 2005
EXTENSIONS
More terms from Emeric Deutsch, Apr 10 2006
STATUS
approved