OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 845
FORMULA
E.g.f.: -x/(-1+x)*(exp(-x/(-1+x))-1)
D-finite Recurrence: {a(1)=0, a(0)=0, a(2)=2, (-n^4-6*n^3-11*n^2-6*n)*a(n)+(3*n^3+18*n^2+33*n+18)*a(n+1)+(-3*n^2-14*n-15)*a(n+2)+(n+2)*a(n+3)=0}
a(n) ~ n^(n+1/4)*exp(2*sqrt(n)-n-1/2)/sqrt(2). - Vaclav Kotesovec, Sep 30 2013
a(n) = n!*(LaguerreL(n - 1, -1) - 1) for n >= 1. - Peter Luschny, Mar 28 2023
MAPLE
spec := [S, {C=Sequence(Z, 1 <= card), B=Set(C, 1 <= card), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
# Alternative:
seq(`if`(n=0, 0, simplify(n!*(LaguerreL(n - 1, -1) - 1))), n = 0..18); # Peter Luschny, Mar 28 2023
MATHEMATICA
CoefficientList[Series[-x/(-1+x)*(E^(-x/(-1+x))-1), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name, using e.g.f., from Vaclav Kotesovec, Sep 30 2013
STATUS
approved