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A108217 a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2. 4
1, 1, 3, 7, 26, 126, 744, 5160, 41040, 367920, 3669120, 40279680, 482630400, 6266937600, 87657292800, 1313901388800, 21009968179200, 356995102464000, 6423296495616000, 122000787836928000, 2439304381882368000, 51212587272118272000, 1126433629785784320000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

LINKS

Table of n, a(n) for n=0..22.

Index entries for sequences related to factorial base representation

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

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

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

Sequence in context: A057005 A158561 A252786 * A120120 A126472 A019059

Adjacent sequences:  A108214 A108215 A108216 * A108218 A108219 A108220

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

Corrected by Georg Fischer, May 09 2021

STATUS

approved

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Last modified July 2 14:26 EDT 2022. Contains 355007 sequences. (Running on oeis4.)