A052874 E.g.f.: -x/(-1+x)*(exp(-x/(-1+x))-1).

0, 0, 2, 15, 112, 925, 8556, 88249, 1007056, 12612681, 172092340, 2541367741, 40385290584, 687120886621, 12461362029676, 239945693311185, 4888311943969696, 105038684764873489, 2373935421890157156, 56288808913905658981, 1397063652149884343080, 36219993180755369947941

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

Table of n, a(n) for n=0..21.

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

Sequence in context: A342963 A022026 A026113 * A360432 A376327 A074622

Adjacent sequences: A052871 A052872 A052873 * A052875 A052876 A052877

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