A052585 E.g.f. 1/(1-x-2*x^2).

1, 1, 6, 30, 264, 2520, 30960, 428400, 6894720, 123742080, 2478470400, 54486432000, 1308153369600, 34005760588800, 952248474777600, 28566146568960000, 914137612996608000, 31080323154456576000, 1118898035934142464000, 42518003720397004800000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Laguerre transform is A052563. - Paul Barry, Aug 08 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..350
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 530

Crossrefs

Cf. A080599, A005442.

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1 -x -2*x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 17 2018

Maple

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

Mathematica

With[{m = 50}, CoefficientList[Series[-1/(-1 + x + 2*x^2), {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 17 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1 -x -2*x^2))) \\ G. C. Greubel, May 17 2018

Formula

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

Recurrence: a(1)=1, a(0)=1, (-2*n^2-6*n-4)*a(n)+(-2-n)*a(n+1)+a(n+2)=0.

a(n) = Sum(1/9*(1+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^2))*n!.

a(n) = n!*A001045(n+1). - Paul Barry, Aug 08 2008

a(n) = D^n(1/(1-x)) evaluated at x = 0, where D is the operator sqrt(1+8*x)*d/dx. Cf. A080599 and A005442. - Peter Bala, Dec 07 2011

Extensions

a(18)-a(19) added by G. C. Greubel, May 17 2018