A052694 Expansion of e.g.f. (1 + x^3 - 2*x^4)/(1-2*x).

1, 2, 8, 54, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200, 81749606400, 1961990553600, 51011754393600, 1428329123020800, 42849873690624000, 1371195958099968000, 46620662575398912000

Offset

0,2

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 643

Formula

E.g.f.: (1 + x^3 - 2*x^4)/(1-2*x).

D-finite Recurrence: a(0)=1, a(1)=2, a(2)=8, a(3)=54, a(4)=384, a(n) = 2*n*a(n-1).

a(n) = 2^n*n! + 6*[n=3].

G.f.: 6*x^3 + Hypergeometric2F0([1,1], [], 2*x). - G. C. Greubel, Jun 01 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1+x^3-2x^4)/(1-2x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 12 2014 *)

Prog

(Magma) [n eq 3 select 54 else 2^n*Factorial(n): n in [0..30]]; // G. C. Greubel, Jun 01 2022
(SageMath) [2^n*factorial(n) + 6*bool(n==3) for n in (0..30)] # G. C. Greubel, Jun 01 2022

Crossrefs

Cf. A000079, A000142.

Sequence in context: A197931 A296788 A079503 * A069729 A346647 A354690

Adjacent sequences: A052691 A052692 A052693 * A052695 A052696 A052697

Keyword

easy,nonn

Author

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

Status

approved