OFFSET
1,1
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.83)
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..150
Alexander Burstein and Louis W. Shapiro, Pseudo-involutions in the Riordan group, arXiv:2112.11595 [math.CO], 2021.
N. J. A. Sloane, Transforms
FORMULA
Divides by n and shifts left under exponential transform.
E.g.f.: A(x) = x-LambertW(-x*exp(x)). - Vladeta Jovovic, Mar 08 2003
a(n) = Sum_{k=0..n} (binomial(n, k)*(n-k)^(n-1)).
A(x) = 2*compositional inverse of 2*x/(1+exp(2*x)). - Peter Bala, Oct 14 2011
a(n) ~ n^(n-1) * sqrt((1+LambertW(1/e))) / (e*LambertW(1/e))^n. - Vaclav Kotesovec, Nov 30 2012
MAPLE
a:= n-> add(binomial(n, k)*(n-k)^(n-1), k=0..n):
seq(a(n), n=1..20); # Alois P. Heinz, Nov 30 2012
MATHEMATICA
Table[n!*Sum[2^j/j!*StirlingS2[n-1, n-j], {j, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Nov 30 2012 *)
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Jan 04 1999
STATUS
approved