A052698 Expansion of e.g.f. x/((1-x)*(1-3*x)).

0, 1, 8, 78, 960, 14520, 262080, 5508720, 132249600, 3571102080, 107136691200, 3535550726400, 127280305152000, 4963938127948800, 208485488552140800, 9381848292520704000, 450328738963783680000, 22966766042840395776000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..375

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 648

Formula

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

D-finite Recurrence: a(0) = 0, a(1)=1, a(n) = 4*n*a(n-1) - 3*n*(n-1)*a(n-2).

a(n) = (3^n - 1)*n!/2.

a(n) = n!*A003462(n). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[x/((1-x)(1-3x)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 05 2014 *)
Table[(3^n-1)*n!/2, {n, 0, 30}] (* G. C. Greubel, May 31 2022 *)

Prog

(SageMath) [(3^n-1)*factorial(n)/2 for n in (0..30)] # G. C. Greubel, May 31 2022

Crossrefs

Cf. A003462.

Sequence in context: A132164 A058480 A000435 * A052603 A071556 A316203

Adjacent sequences: A052695 A052696 A052697 * A052699 A052700 A052701

Keyword

easy,nonn

Author

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

Status

approved