%I #17 Aug 20 2021 07:10:45
%S 0,0,0,0,0,0,720,7560,50400,272160,1300320,5738040,23958000,96061680,
%T 373477104,1417295880,5274360000,19313985600,69770966976,249130574424,
%U 880629138000
%N E.g.f.: x^3*(exp(x)-1)^3.
%C Previous name was: A simple grammar.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=741">Encyclopedia of Combinatorial Structures 741</a>
%F E.g.f.: x^3*exp(x)^3-3*x^3*exp(x)^2+3*x^3*exp(x)-x^3 = x^3*(exp(x)-1)^3.
%F D-finite Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (-36*n^2-66*n-6*n^3-36)*a(n)+(-44*n+11*n^3+33*n^2-132)*a(n+1)+(-6*n^3-36+42*n)*a(n+2)+(-3*n^2+n^3+2*n)*a(n+3)=0}
%F For n>3 , a(n) = (n-2)*(n-1)*n*(3^(n-3) - 3*2^(n-3) + 3). - _Vaclav Kotesovec_, Oct 01 2013
%p spec := [S,{B=Set(Z,1 <= card),S=Prod(Z,Z,Z,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[x^3*(E^x-1)^3, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2013 *)
%K easy,nonn
%O 0,7
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name, using e.g.f., by _Vaclav Kotesovec_, Oct 01 2013