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Permutations with exactly 12 fixed points.
3

%I #22 Jul 06 2023 05:19:27

%S 1,0,91,910,16380,272272,4919460,93419352,1868513010,39238479280,

%T 863247190806,19854684036460,476512419579196,11912810484279600,

%U 309733072600927300,8362792960207653240,234158202885844712475

%N Permutations with exactly 12 fixed points.

%H Vincenzo Librandi, <a href="/A129255/b129255.txt">Table of n, a(n) for n = 12..200</a>

%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for sequences related to permutations with fixed points</a>

%F E.g.f.: exp(-x)/(1-x)*(x^12/12!). [_Zerinvary Lajos_, Apr 03 2009]

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

%p a:=n->sum(n!*sum((-1)^k/(k-11)!, j=0..n), k=11..n): seq(-a(n)/12!, n=11..28);

%p 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

%t 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 *)

%o (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^12/12!)) ) \\ _Joerg Arndt_, Feb 19 2014

%Y Column k=12 of A008290.

%Y Cf. A008291, A170942.

%K nonn

%O 12,3

%A _Zerinvary Lajos_, May 25 2007

%E Changed offset from 0 to 12 by _Vincenzo Librandi_, Feb 19 2014

%E Edited by _Joerg Arndt_, Feb 19 2014