A129217 Permutations with exactly 9 fixed points.

1, 0, 55, 440, 6435, 88088, 1326325, 21209760, 360590230, 6490575520, 123321027258, 2466420377200, 51794828215130, 1139486220235440, 26208183066232310, 628996393588267936, 15724909839708741375

Offset

9,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 9..200

Index entries for sequences related to permutations with fixed points

Formula

a(n) = A008290(n,9).

E.g.f.: exp(-x)/(1-x)*(x^9/9!). [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/9!)*Sum_{k>=9} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

Maple

a:=n->sum(n!*sum((-1)^k/(k-8)!, j=0..n), k=8..n): seq(a(n)/9!, n=8..27);
restart: G(x):=exp(-x)/(1-x)*(x^9/9!): 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=9..25); # Zerinvary Lajos, Apr 03 2009

Mathematica

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^9/9!, {x, 0, nn}], x]Range[0, nn]!, 9]] (* 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: A380070 A340240 A355511 * A116060 A145054 A166839

Adjacent sequences: A129214 A129215 A129216 * A129218 A129219 A129220

Keyword

nonn

Author

Zerinvary Lajos, May 25 2007

Extensions

Changed offset from 0 to 9 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014

Status

approved