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%I #24 Apr 18 2017 07:03:54
%S 1,3,24,288,4608,92160,2211840,61931520,1981808640,71345111040,
%T 2853804441600,125567395430400,6027234980659200,313416218994278400,
%U 17551308263679590400,1053078495820775424000,67397023732529627136000
%N E.g.f. (1-x)/(1-4x).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=537">Encyclopedia of Combinatorial Structures 537</a>
%F E.g.f.: (-1+x)/(-1+4*x).
%F Recurrence: {a(0)=1, a(1)=3, (-4-4*n)*a(n) + a(n+1)=0}.
%F a(n) = 3*4^(n-1)*n!, n>0.
%p spec := [S,{S=Sequence(Prod(Sequence(Z),Union(Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t s=3;lst={1, s};Do[s+=n*s+s;AppendTo[lst, s], {n, 6, 5!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t With[{nn=20},CoefficientList[Series[(1-x)/(1-4x),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Nov 26 2011 *)
%o (PARI) Vec(serlaplace((-1+x)/(-1+4*x)+ O(x^30))) \\ _Michel Marcus_, Jan 09 2015
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000