A052617 E.g.f. (1+x-x^2)/((1-x)(1-2x)).

1, 4, 18, 114, 936, 9480, 114480, 1607760, 25764480, 464123520, 9286099200, 204334099200, 4904497382400, 127523158963200, 3570735629260800, 107123376552192000, 3427968972460032000, 116551300751069184000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 562

Programs

Maple

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

Mathematica

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 *)

Formula

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

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}

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

a(n)=n!*A052549(n). - R. J. Mathar, Jun 03 2022