OFFSET
0,3
COMMENTS
Inverse binomial transform of A000312. - Tilman Neumann, Dec 13 2008
The |a(n)| is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the digraph representation of f has no isolated vertices. (* Geoffrey Critzer, Nov 13 2011 *)
REFERENCES
sci.math article 3CBC2B66.224E(AT)olympus.mons
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = n! * Sum_{k=0..n} (-1)^k*k^k/(k!*(n - k)!).
E.g.f. for absolute value of {a(n)}: exp(C(x)-x) where C(x) is the e.g.f for A001865. - Geoffrey Critzer, Nov 13 2011, corrected by Vaclav Kotesovec, Nov 27 2012
abs(a(n)) ~ (exp(1)*n-1/2)/exp(1+exp(-1)) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012
a(n) = (-1)^n * A350212(n,0). - Alois P. Heinz, Dec 19 2021
MATHEMATICA
t = Sum[n^(n - 1) x^n/n!, {n, 1, 20}]; Range[0, 20]! CoefficientList[Series[Exp[-x]/(1 - t), {x, 0, 20}], x] (* Geoffrey Critzer, Nov 13 2011 *)
Range[0, 18]! CoefficientList[ Series[ Exp[x]/(1 + LambertW[x]), {x, 0, 18}], x] (* Robert G. Wilson v, Nov 28 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)/(1+lambertw(x)))) \\ G. C. Greubel, Jun 11 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Joe Keane (jgk(AT)jgk.org), May 03 2002
STATUS
approved