A129255 Permutations with exactly 12 fixed points.

1, 0, 91, 910, 16380, 272272, 4919460, 93419352, 1868513010, 39238479280, 863247190806, 19854684036460, 476512419579196, 11912810484279600, 309733072600927300, 8362792960207653240, 234158202885844712475

Offset: 12

Author

Zerinvary Lajos, May 25 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 12..200
• Index entries for sequences related to permutations with fixed points

Crossrefs

Column k=12 of A008290.

Cf. A008291, A170942.

Programs

Maple

a:=n->sum(n!*sum((-1)^k/(k-11)!, j=0..n), k=11..n): seq(-a(n)/12!, n=11..28);
restart: G(x):=exp(-x)/(1-x)*(x^12/12!): 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=12..28);# Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^12/12!, {x, 0, nn}], x]Range[0, nn]!, 12]] (* Vincenzo Librandi, Feb 19 2014 *)

PARI

x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^12/12!)) ) \\ Joerg Arndt, Feb 19 2014

Formula

E.g.f.: exp(-x)/(1-x)*(x^12/12!). [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/12!)*Sum_{k>=12} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

Extensions

Changed offset from 0 to 12 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014