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

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 618

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

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 *)

Prog

(Magma) [0, 0] cat [4^(n-2)*Factorial(n): n in [2..30]]; // G. C. Greubel, Jun 13 2022
(SageMath) [(4^(n-2) - 4^(n-2)*bool(n<2))*factorial(n) for n in (0..30)] # G. C. Greubel, Jun 13 2022

Crossrefs

Cf. A000142, A000302.

Sequence in context: A188953 A081685 A288944 * A052736 A103904 A219431

Adjacent sequences: A052667 A052668 A052669 * A052671 A052672 A052673

Keyword

easy,nonn

Author

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

Status

approved