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

10,3

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A008290, A008291, A170942.

Sequence in context: A202639 A175260 A233065 * A046409 A128952 A282050

Adjacent sequences: A129215 A129216 A129217 * A129219 A129220 A129221

Keyword

nonn

Author

Zerinvary Lajos, May 25 2007

Extensions

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

Edited by Joerg Arndt, Feb 19 2014

Status

approved