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%I #20 Mar 28 2023 08:25:26
%S 0,0,2,15,112,925,8556,88249,1007056,12612681,172092340,2541367741,
%T 40385290584,687120886621,12461362029676,239945693311185,
%U 4888311943969696,105038684764873489,2373935421890157156,56288808913905658981,1397063652149884343080,36219993180755369947941
%N E.g.f.: -x/(-1+x)*(exp(-x/(-1+x))-1).
%C Previous name was: A simple grammar.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=845">Encyclopedia of Combinatorial Structures 845</a>
%F E.g.f.: -x/(-1+x)*(exp(-x/(-1+x))-1)
%F 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}
%F a(n) ~ n^(n+1/4)*exp(2*sqrt(n)-n-1/2)/sqrt(2). - _Vaclav Kotesovec_, Sep 30 2013
%F a(n) = n!*(LaguerreL(n - 1, -1) - 1) for n >= 1. - _Peter Luschny_, Mar 28 2023
%p 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);
%p # Alternative:
%p seq(`if`(n=0, 0, simplify(n!*(LaguerreL(n - 1, -1) - 1))), n = 0..18); # _Peter Luschny_, Mar 28 2023
%t CoefficientList[Series[-x/(-1+x)*(E^(-x/(-1+x))-1), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name, using e.g.f., from _Vaclav Kotesovec_, Sep 30 2013