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%I #20 Aug 11 2017 17:27:12
%S 0,0,2,18,96,600,4320,35280,322560,3265920,36288000,439084800,
%T 5748019200,80951270400,1220496076800,19615115520000,334764638208000,
%U 6046686277632000,115242726703104000,2311256907767808000
%N E.g.f. x^2*(1+x-x^2)/(1-x)^2.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=579">Encyclopedia of Combinatorial Structures 579</a>
%F E.g.f.: -x^2*(-x+x^2-1)/(-1+x)^2.
%F Recurrence: {a(0)=0, a(1)=0, a(2)=2, a(3)=18; for n > 3, a(n) = a(n-1)*n^2/(n-1)}. [Simplified by _Jon E. Schoenfield_, Aug 11 2017]
%F For n > 2, a(n) = n*n!.
%p spec := [S,{S=Prod(Z,Z,Sequence(Z),Union(Z,Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p restart:printlevel := -1; a := [0]; T := x->LambertW(-x); f := series(((1+T(x)))/(1-T(x)), x, 24); for m from 1 to 19 do a := [op(a), op(2*m, f)*m! ] od; print(a); # _Zerinvary Lajos_, Mar 28 2009
%t With[{nn=20},CoefficientList[Series[x^2 (1+x-x^2)/(1-x)^2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 27 2016 *)
%Y Essentially the same as A001563.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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