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A129217 Permutations with exactly 9 fixed points.

%I A129217 #19 Jul 06 2023 05:22:38
%S A129217 1,0,55,440,6435,88088,1326325,21209760,360590230,6490575520,
%T A129217 123321027258,2466420377200,51794828215130,1139486220235440,
%U A129217 26208183066232310,628996393588267936,15724909839708741375
%N A129217 Permutations with exactly 9 fixed points.
%H A129217 Vincenzo Librandi, <a href="/A129217/b129217.txt">Table of n, a(n) for n = 9..200</a>
%H A129217 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for sequences related to permutations with fixed points</a>
%F A129217 a(n) = A008290(n,9).
%F A129217 E.g.f.: exp(-x)/(1-x)*(x^9/9!). [_Zerinvary Lajos_, Apr 03 2009]
%F A129217 O.g.f.: (1/9!)*Sum_{k>=9} k!*x^k/(1 + x)^(k+1). - _Ilya Gutkovskiy_, Apr 15 2017
%p A129217 a:=n->sum(n!*sum((-1)^k/(k-8)!, j=0..n), k=8..n): seq(a(n)/9!, n=8..27);
%p A129217 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
%t A129217 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 *)
%o A129217 (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^9/9!)) ) \\ _Joerg Arndt_, Feb 19 2014
%Y A129217 Cf. A008290, A008291, A170942.
%K A129217 nonn
%O A129217 9,3
%A A129217 _Zerinvary Lajos_, May 25 2007
%E A129217 Changed offset from 0 to 9 by _Vincenzo Librandi_, Feb 19 2014
%E A129217 Edited by _Joerg Arndt_, Feb 19 2014