A052617 - OEIS

%I #15 Jun 03 2022 18:50:26

%S 1,4,18,114,936,9480,114480,1607760,25764480,464123520,9286099200,

%T 204334099200,4904497382400,127523158963200,3570735629260800,

%U 107123376552192000,3427968972460032000,116551300751069184000

%N E.g.f. (1+x-x^2)/((1-x)(1-2x)).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=562">Encyclopedia of Combinatorial Structures 562</a>

%F E.g.f.: -(-x+x^2-1)/(-1+2*x)/(-1+x)

%F Recurrence: {a(0)=1, a(1)=4, (2*n^2+6*n+4)*a(n) +(-6-3*n)*a(n+1) +a(n+2)=0, a(2)=18}

%F (-1+5*2^(n-1))*n!, n>0.

%F a(n)=n!*A052549(n). - _R. J. Mathar_, Jun 03 2022

%p spec := [S,{S=Prod(Union(Z,Sequence(Z)),Sequence(Union(Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t With[{nn=20},CoefficientList[Series[(1+x-x^2)/((1-x)(1-2x)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 25 2018 *)

%K easy,nonn

%O 0,2

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000