A052660 E.g.f. (2-2x-x^2)/((1-x)(1-x-x^2)).

2, 2, 6, 24, 144, 1080, 10080, 110880, 1411200, 20321280, 326592000, 5787936000, 112086374400, 2353813862400, 53265935923200, 1291982275584000, 33434618241024000, 919452001628160000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 607

Programs

Maple

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

Formula

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

Recurrence: {a(1)=2, a(2)=6, a(0)=2, (n^3+6*n^2+11*n+6)*a(n)+(-2*n-6)*a(n+2)+a(n+3)=0}

(1+Sum(1/5*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^2)))*n!

a(n) = n!*A001611(n+1). - R. J. Mathar, Nov 27 2011