A060008 a(n) = 9*binomial(n,4) = 3n*(n-1)*(n-2)*(n-3)/8.

0, 0, 0, 0, 9, 45, 135, 315, 630, 1134, 1890, 2970, 4455, 6435, 9009, 12285, 16380, 21420, 27540, 34884, 43605, 53865, 65835, 79695, 95634, 113850, 134550, 157950, 184275, 213759, 246645, 283185, 323640, 368280, 417384, 471240, 530145, 594405

Offset

0,5

Comments

Number of permutations of n letters where exactly four change position.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

Equals 3*A050534. - Zerinvary Lajos, Feb 12 2007

G.f.: 9*x^4/(1-x)^5. - Colin Barker, Jul 02 2012

From Amiram Eldar, Jul 19 2022: (Start)

Sum_{n>=4} 1/a(n) = 4/27.

Sum_{n>=4} (-1)^n/a(n) = 32*log(2)/9 - 64/27. (End)

Example

a(6) = 135 since there are 15 ways to choose the four points that move and 9 ways to move them and 15*9 = 135.

Mathematica

9*Binomial[Range[0, 40], 4] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 0, 9}, 40] (* Harvey P. Dale, Jun 09 2014 *)

Prog

(PARI) { for (n=0, 1000, write("b060008.txt", n, " ", 3*n*(n - 1)*(n - 2)*(n - 3)/8); ) } \\ Harry J. Smith, Jul 01 2009

Crossrefs

For changing 0, 1, 2, 3, 4, 5, n-4, n elements see A000012, A000004, A000217 (offset), A007290, A060008, A060836, A000475, A000166. Also see A000332, A008290.

A diagonal of A008291.

Sequence in context: A188351 A220443 A289721 * A212089 A212142 A095166

Adjacent sequences: A060005 A060006 A060007 * A060009 A060010 A060011

Keyword

easy,nonn

Author

Henry Bottomley, Mar 16 2001

Status

approved