A052670 Expansion of e.g.f. x^2/(1-4*x).

0, 0, 2, 24, 384, 7680, 184320, 5160960, 165150720, 5945425920, 237817036800, 10463949619200, 502269581721600, 26118018249523200, 1462609021973299200, 87756541318397952000, 5616418644377468928000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..350
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 618

Crossrefs

Cf. A000142, A000302.

Programs

Magma

[0,0] cat [4^(n-2)*Factorial(n): n in [2..30]]; // G. C. Greubel, Jun 13 2022

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[x^2/(1-4x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 27 2015 *)

SageMath

[(4^(n-2) - 4^(n-2)*bool(n<2))*factorial(n) for n in (0..30)] # G. C. Greubel, Jun 13 2022

Formula

E.g.f.: x^2/(1 - 4*x)

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

a(n) = 4^(n-2) * n!, n>1.

G.f.: 2*x^2*Hypergeometric2F0([3,1], [], 4*x). - G. C. Greubel, Jun 13 2022