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A129136 Permutations with exactly 6 fixed points. 9
1, 0, 28, 168, 1890, 20328, 244860, 3181464, 44543499, 668147480, 10690367688, 181736238320, 3271252308324, 62153793831024, 1243075876659240, 26104593409789776, 574301055015449685, 13208924265355241808 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 6..200

FindStat - Combinatorial Statistic Finder, The number of fixed points of a permutation

FORMULA

E.g.f.: exp(-x)/(1-x)*(x^6/6!). [Zerinvary Lajos, Apr 03 2009]

O.g.f.: (1/6!)*Sum_{k>=6} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017

MAPLE

a:=n->sum(n!*sum((-1)^k/(k-5)!, j=0..n), k=5..n): seq(-a(n)/6!, n=5..24);

restart: G(x):=exp(-x)/(1-x)*(x^6/6!): 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=6..23); # Zerinvary Lajos, Apr 03 2009

MATHEMATICA

With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^6/6!, {x, 0, nn}], x]Range[0, nn]!, 6]] (* Vincenzo Librandi, Feb 19 2014 *)

PROG

(PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^6/6!)) ) \\ Joerg Arndt, Feb 19 2014

CROSSREFS

Cf. A008290, A000166, A000240, A000387, A000449, A000475, A129135, A129149, A129153, A129217, A129218, A129238, A129255, A008291, A170942.

Sequence in context: A219298 A197967 A305270 * A042528 A219821 A219386

Adjacent sequences:  A129133 A129134 A129135 * A129137 A129138 A129139

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, May 25 2007

EXTENSIONS

Changed offset from 0 to 6 by Vincenzo Librandi, Feb 19 2014

Edited by Joerg Arndt, Feb 19 2014

STATUS

approved

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Last modified May 30 09:21 EDT 2020. Contains 334717 sequences. (Running on oeis4.)