A052563 E.g.f.: (1-x)/(1-3*x).

1, 2, 12, 108, 1296, 19440, 349920, 7348320, 176359680, 4761711360, 142851340800, 4714094246400, 169707392870400, 6618588321945600, 277980709521715200, 12509131928477184000, 600438332566904832000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Laguerre transform of A052585. - Paul Barry, Aug 08 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..375
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 505

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)/(1-3*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 23 2018

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-x)/(1-3x),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, May 21 2014 *)

PARI

x='x+O('x^30); Vec(serlaplace((1-x)/(1-3*x))) \\ G. C. Greubel, May 23 2018

Formula

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

Recurrence: {a(0)=1, a(1)=2, (-3*n-3)*a(n)+a(n+1)=0}

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

a(n) = Sum_{k=0..n} binomial(n,k)(n!/k!)k!*A001045(k+1). - Paul Barry, Aug 08 2008