A052661 E.g.f. (2-3x)/((1-x)(1-x-x^2)).

2, 1, 4, 12, 72, 480, 4320, 45360, 564480, 7983360, 127008000, 2235340800, 43110144000, 902918016000, 20399720140800, 494300911104000, 12783824621568000, 351419178958848000, 10230993181753344000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..417
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 608

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(2-3x)/((1-x)(1-x-x^2)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 25 2023 *)

Formula

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

Recurrence: {a(1)=1, a(2)=4, 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+3*_alpha)*_alpha^(-1-n), _alpha =RootOf(-1+_Z+_Z^2)))*n!

a(n) = n!*A001611(n-1), n>0. - R. J. Mathar, Nov 27 2011