OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..369
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 842
FORMULA
E.g.f.: -LambertW(x/(-1+x))
a(n) = Sum_{k=1..n} (n!/k!)*binomial(n-1, k-1)*k^(k-1). - Vladeta Jovovic, Sep 17 2003
a(n) ~ (1+exp(-1))^(n+1/2)*n^(n-1). - Vaclav Kotesovec, Sep 30 2013
From Seiichi Manyama, Sep 10 2024: (Start)
E.g.f. A(x) satisfies A(x) = x * (A(x) + exp(A(x))).
E.g.f.: Series_Reversion( x / (x + exp(x)) ). (End)
MAPLE
spec := [S, {C=Sequence(Z, 1 <= card), B=Set(S), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[-LambertW[x/(-1+x)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(Maxima) makelist(sum((n!/k!)*binomial(n-1, k-1)*k^(k-1), k, 1, n), n, 0, 17); /* Bruno Berselli, May 25 2011 */
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(x/(-1+x))) )) \\ G. C. Greubel, Nov 08 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f., Vaclav Kotesovec, Sep 30 2013
STATUS
approved