A052686 Expansion of e.g.f. x^2*(1+3*x-3*x^2)/(1-x).

0, 0, 2, 24, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 634

Formula

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

Recurrence: a(0)=0, a(1)=0, a(2)=2, a(3)=24, a(4)=24, a(n) = n*a(n-1).

a(n) = n!, n>3.

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(x^2 (1+3x-3x^2))/(1-x), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, May 05 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); [0, 0] cat Coefficients(R!(Laplace( x^2*(1+3*x-3*x^2)/(1-x) ))); // G. C. Greubel, Jun 03 2022
(SageMath) [factorial(n) -bool(n==0) -bool(n==1) +18*bool(n==3) for n in (0..30)] # G. C. Greubel, Jun 03 2022

Crossrefs

Cf. A000142.

Sequence in context: A072217 A229429 A281139 * A258781 A371207 A064818

Adjacent sequences: A052683 A052684 A052685 * A052687 A052688 A052689

Keyword

easy,nonn

Author

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

Status

approved