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

0,1

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 593

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

Maple

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

Crossrefs

Sequence in context: A300641 A078433 A059494 * A326983 A232974 A181334

Adjacent sequences: A052644 A052645 A052646 * A052648 A052649 A052650

Keyword

easy,nonn

Author

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

Status

approved