A108217 a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.

1, 1, 3, 7, 26, 126, 744, 5160, 41040, 367920, 3669120, 40279680, 482630400, 6266937600, 87657292800, 1313901388800, 21009968179200, 356995102464000, 6423296495616000, 122000787836928000, 2439304381882368000, 51212587272118272000, 1126433629785784320000

Offset: 0

Author

Miklos Kristof, following a suggestion from Peter Boros, (borospet(AT)freemail.hu), Jun 16 2005

Keywords

• easy
• nonn

Comments

In factorial base representation (A007623) the terms of this sequence look as: 1, 1, 11, 101, 1010, 10100, 101000, ... From a(3)=7 onward each term begins always with "101", which is then followed by n-3 zeros. - Antti Karttunen, Sep 23 2016

Examples

			a(6) = 6!+4! = 720+24 = 744.
		

Links

• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A000142, A002061, A007623, A001048, A030495.

Row 5 of A276955, from term a(3)=7 onward.

Programs

Maple

a:= n-> `if`(n<2, 1, n!+(n-2)!):
seq(a(n), n=0..30);

Mathematica

Table[If[n<2,1,n!+(n-2)!],{n,0,30}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
Join[{1,1},#[[1]]+#[[3]]&/@Partition[Range[0,20]!,3,1]] (* Harvey P. Dale, Nov 19 2015 *)

Scheme

(define (A108217 n) (if (<= n 1) 1 (* (A002061 n) (A000142 (- n 2))))) ;; Antti Karttunen, Sep 23 2016

Formula

For n >= 2, a(n) = A002061(n) * (n-2)! - Antti Karttunen, Sep 23 2016

E.g.f.: x + (1-x)*log(1-x) + 1/(1-x). - Andrew Howroyd, May 09 2021

Extensions

Corrected by Georg Fischer, May 09 2021