A052699 Expansion of e.g.f. (1+x^5-x^6)/(1-x).

1, 1, 2, 6, 24, 240, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 649

Crossrefs

Cf. A000142.

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1+x^5-x^6)/(1-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 04 2014 *)
Table[n! + 5!*Boole[n==5], {n, 0, 40}] (* G. C. Greubel, May 31 2022 *)

SageMath

[factorial(n) + factorial(5)*bool(n==5) for n in (0..30)] # G. C. Greubel, May 31 2022

Formula

E.g.f.: (1+x^5-x^6)/(1-x).

a(n+1) = (n+1)*a(n), for n > 5.

a(n) = n! + 5!*[n=5].