A052690 Expansion of e.g.f. x*(1+x-3*x^2)/(1-3*x).

0, 1, 8, 54, 648, 9720, 174960, 3674160, 88179840, 2380855680, 71425670400, 2357047123200, 84853696435200, 3309294160972800, 138990354760857600, 6254565964238592000, 300219166283452416000, 15311177480456073216000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..350

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 638

Formula

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

Recurrence: a(0)=0, a(1)=1, a(2)=8, a(n) = 3*n*a(n-1).

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

G.f.: -1/3 + 2*x^2 + Hypergeometric2F0([1,1], [], 3*x). - G. C. Greubel, Jun 02 2022

Maple

spec := [S, {S=Prod(Z, Union(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-3x^2)/(1-3x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 05 2018 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); [0] cat Coefficients(R!(Laplace( x*(1+x-3*x^2)/(1-3*x) ))); // G. C. Greubel, Jun 02 2022
(SageMath) [3^(n-1)*factorial(n) -bool(n==0)/3 +2*bool(n==2) for n in (0..30)] # G. C. Greubel, Jun 02 2022

Crossrefs

Cf. A000142, A000244.

Sequence in context: A134825 A279854 A241581 * A304589 A027525 A298654

Adjacent sequences: A052687 A052688 A052689 * A052691 A052692 A052693

Keyword

easy,nonn

Author

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

Status

approved