A060836 - OEIS

%I #15 Dec 26 2024 15:20:44

%S 0,0,0,0,44,264,924,2464,5544,11088,20328,34848,56628,88088,132132,

%T 192192,272272,376992,511632,682176,895356,1158696,1480556,1870176,

%U 2337720,2894320,3552120,4324320,5225220,6270264,7476084,8860544,10442784,12243264,14283808,16587648

%N Number of permutations of n letters where exactly 5 change position.

%H Harry J. Smith, <a href="/A060836/b060836.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

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

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

%F G.f.: 44*x^5/(1 - x)^6. - _Colin Barker_, Apr 22 2012

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

%o (PARI) a(n) = { 44*binomial(n, 5) } \\ _Harry J. Smith_, Jul 19 2009

%Y 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.

%Y Rencontre sequences are A000166 A000240 A000387 A000449 and A000475.

%Y A diagonal of A008291.

%K nonn,easy

%O 1,5

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