A129218 Permutations with exactly 10 fixed points.

1, 0, 66, 572, 9009, 132132, 2122120, 36056592, 649062414, 12332093488, 246642054516, 5179482792120, 113948622073286, 2620818306541512, 62899639358957544, 1572490983970669840, 40884765583242727575

Offset: 10

Author

Zerinvary Lajos, May 25 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 10..200

Crossrefs

Cf. A008290, A008291, A170942.

Programs

Maple

a:=n->sum(n!*sum((-1)^k/(k-9)!, j=0..n), k=9..n): seq(-a(n)/10!, n=9..27);
restart: G(x):=exp(-x)/(1-x)*(x^10/10!): 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=10..26); # Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^10/10!, {x, 0, nn}], x]Range[0, nn]!, 10]] (* Vincenzo Librandi, Feb 19 2014 *)

PARI

x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^9/9!)) ) \\ Joerg Arndt, Feb 19 2014

Formula

a(n) = A008290(n,10).

E.g.f.: exp(-x)/(1-x)*(x^10/10!). [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/10!)*Sum_{k>=10} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

Extensions

Changed offset from 0 to 10 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014