A052639 E.g.f. (1-2x)/(1-2x-x^3).

1, 0, 0, 6, 48, 480, 6480, 100800, 1774080, 35199360, 776563200, 18840729600, 498640665600, 14297239756800, 441470866636800, 14605415016192000, 515412006100992000, 19325209343311872000, 767215648278503424000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 585

Programs

Maple

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

Formula

E.g.f.: (-1+2*x)/(-1+2*x+x^3)

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

Sum(-1/59*(8+6*_alpha^2-25*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^3))*n!

a(n)= n!*A008998(n-3), n>2. - R. J. Mathar, Nov 27 2011