A129238 Permutations with exactly 11 fixed points.

1, 0, 78, 728, 12285, 192192, 3279640, 59001696, 1121107806, 22421988160, 470862104076, 10358965584240, 238256209789598, 5718149032454208, 142953725815812600, 3716796871203401440, 100353515522504876775

Offset: 11

Author

Zerinvary Lajos, May 25 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 11..200
• 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-10)!, j=0..n), k=10..n): seq(a(n)/11!, n=10..27);
restart: G(x):=exp(-x)/(1-x)*(x^11/11!): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=11..27); # Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^11/11!, {x, 0, nn}], x]Range[0, nn]!, 11]] (* Vincenzo Librandi, Feb 19 2014 *)

PARI

x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^11/11!)) ) \\ Joerg Arndt, Feb 19 2014

Formula

a(n) = A008290(n,11).

E.g.f.: exp(-x)/(1-x)*(x^11/11!) . [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/11!)*Sum_{k>=11} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

Extensions

Changed offset from 0 to 11 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014