A052561 a(n) = (1 + 2^n) * n!.

2, 3, 10, 54, 408, 3960, 46800, 650160, 10362240, 186157440, 3719520000, 81789523200, 1962469555200, 51017981414400, 1428416301312000, 42851181364992000, 1371216880889856000, 46621018262827008000

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 503

Formula

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

a(n) = 3*n*a(n-1) - 2*n*(n-1)*a(n-2), with a(0)=2, a(1)=3.

a(n) = A000051(n)*A000142(n). - Michel Marcus, May 05 2019

Maple

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

Mathematica

Table[(1+2^n)*n!, {n, 0, 20}] (* G. C. Greubel, May 05 2019 *)

Prog

(PARI) {a(n) = (1+2^n)*n!}; \\ G. C. Greubel, May 05 2019
(Magma) [(1+2^n)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 05 2019
(Sage) [(1+2^n)*factorial(n) for n in (0..20)] # G. C. Greubel, May 05 2019
(GAP) List([0..20], n-> (1+2^n)*Factorial(n)) # G. C. Greubel, May 05 2019

Crossrefs

Cf. A000051, A000142.

Sequence in context: A013081 A054921 A192258 * A181927 A066526 A093856

Adjacent sequences: A052558 A052559 A052560 * A052562 A052563 A052564

Keyword

easy,nonn

Author

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

Status

approved