A060836 Number of permutations of n letters where exactly 5 change position.

0, 0, 0, 0, 44, 264, 924, 2464, 5544, 11088, 20328, 34848, 56628, 88088, 132132, 192192, 272272, 376992, 511632, 682176, 895356, 1158696, 1480556, 1870176, 2337720, 2894320, 3552120, 4324320, 5225220, 6270264, 7476084, 8860544, 10442784, 12243264, 14283808, 16587648

Offset: 1

Author

Robert Goodhand (rgoodhand(AT)hotmail.com), May 12 2001

Keywords

• nonn
• easy

Examples

			a(8) = a(7) * 8/(8-5) = 924 * 8/3 = 2464.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

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.

Rencontre sequences are A000166 A000240 A000387 A000449 and A000475.

A diagonal of A008291.

Programs

PARI

a(n) = { 44*binomial(n, 5) } \\ Harry J. Smith, Jul 19 2009

Formula

a(n) = 44*binomial(n, 5).

a(n) = a(n-1)*n/(n-5).

G.f.: 44*x^5/(1 - x)^6. - Colin Barker, Apr 22 2012