login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052649 E.g.f. (2+x-x^2)/(1-x)^2. 6
2, 5, 14, 54, 264, 1560, 10800, 85680, 766080, 7620480, 83462400, 997920000, 12933043200, 180583603200, 2702527027200, 43153254144000, 732297646080000, 13160434839552000, 249692574523392000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(1) is 5 and gives the row number in the table of 0-origin permutations of order 3 in which the first 3 items are reversed. Row 5 of this table is 2 1 0. a(2) is 14 and gives the row number in the table of 0-origin permutations of order 4 in which the first three items are reversed. Row 14 of this table is 2 1 0 3.... a(6) is 10800 and gives the row number in the table of 0-origin permutations of order 8 in which the first 3 items are reversed. Row 10800 of this table is 2 1 0 3 4 5 6 7. Et cetera. - Eugene McDonnell (eemcd(AT)mac.com), Dec 03 2004

In factorial base representation (A007623) the terms of this sequence are written as: 10, 21, 210, 2100, 21000, 210000, ... From a(1) = 5 = "21" onward each term begins always with "21", which is then followed by n-1 zeros. - Antti Karttunen, Sep 24 2016

LINKS

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 596

Index entries for sequences related to factorial base representation

FORMULA

a(n) = (3+2*n)*n!.

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

Recurrence: a(0)=2, a(1)=5, (-7*n-5-2*n^2)*a(n)+(3+2*n)*a(n+1)=0 for n>=1.

a(n) = A129326(n), n>1. - R. J. Mathar, Jun 14 2008

a(n) = (n+1)*a(n-1) - 2*A001048(n-1). - Gary Detlefs, Dec 16 2009

a(0) = 2; for n >= 1, a(n) = 2*(n+1)! + n! - Antti Karttunen, Sep 24 2016

MAPLE

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

MATHEMATICA

f[n_] := (3 + 2 n) n!; f[0] = 2; Array[f, 19, 0]

a[n_] := a[n] = a[n - 1]*n (2 n + 3)/(2 n + 1); a[0] = 2; a[1] = 5; Array[ a, 19, 0] ( Robert G. Wilson v *)

With[{nn=20}, CoefficientList[Series[(2+x-x^2)/(1-x)^2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Nov 09 2017 *)

PROG

(PARI) a(n)=if(n<=1, [2, 5][n+1], a(n-1)*(n*(2*n+3))/(2*n+1) );

for(n=0, 11, print1(a(n), ", "))  /* show terms */

(Scheme) (define (A052649 n) (if (zero? n) 2 (+ (A000142 n) (* 2 (A000142 (+ 1 n)))))) ;; Antti Karttunen, Sep 24 2016

CROSSREFS

Cf. A000142, A001048, A129326.

Row 4 of A276955 (from a(1)=5 onward).

Sequence in context: A243787 A275825 A081439 * A267561 A267560 A122594

Adjacent sequences:  A052646 A052647 A052648 * A052650 A052651 A052652

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)