A052647 E.g.f. (2-2x-x^2)/((1-2x)(1-x^2)).

2, 2, 10, 48, 408, 3840, 46800, 645120, 10362240, 185794560, 3719520000, 81749606400, 1962469555200, 51011754393600, 1428416301312000, 42849873690624000, 1371216880889856000, 46620662575398912000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 593

Programs

Maple

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

Formula

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

Recurrence: {a(1)=2, a(2)=10, a(0)=2, (12+2*n^3+12*n^2+22*n)*a(n)+(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)=0}

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

n!*[2^n+(n mod 2)].

a(n) = n!*A052531(n). - R. J. Mathar, Nov 27 2011