A129136 Permutations with exactly 6 fixed points.

1, 0, 28, 168, 1890, 20328, 244860, 3181464, 44543499, 668147480, 10690367688, 181736238320, 3271252308324, 62153793831024, 1243075876659240, 26104593409789776, 574301055015449685, 13208924265355241808

Offset: 6

Author

Zerinvary Lajos, May 25 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..200
• FindStat - Combinatorial Statistic Finder, The number of fixed points of a permutation
• Index entries for sequences related to permutations with fixed points

Crossrefs

Cf. A008290, A008291, A170942.

Programs

Maple

a:=n->sum(n!*sum((-1)^k/(k-5)!, j=0..n), k=5..n): seq(-a(n)/6!, n=5..24);
restart: G(x):=exp(-x)/(1-x)*(x^6/6!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=6..23); # Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^6/6!, {x, 0, nn}], x]Range[0, nn]!, 6]] (* Vincenzo Librandi, Feb 19 2014 *)

PARI

x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^6/6!)) ) \\ Joerg Arndt, Feb 19 2014

Formula

a(n) = A008290(n,6).

E.g.f.: exp(-x)/(1-x)*(x^6/6!). [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/6!)*Sum_{k>=6} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

D-finite with recurrence +(-n+6)*a(n) +n*(n-7)*a(n-1) +n*(n-1)*a(n-2)=0. - R. J. Mathar, Jul 06 2023

Extensions

Changed offset from 0 to 6 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014