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%I #21 Jul 06 2023 05:21:42
%S 1,0,66,572,9009,132132,2122120,36056592,649062414,12332093488,
%T 246642054516,5179482792120,113948622073286,2620818306541512,
%U 62899639358957544,1572490983970669840,40884765583242727575
%N Permutations with exactly 10 fixed points.
%H Vincenzo Librandi, <a href="/A129218/b129218.txt">Table of n, a(n) for n = 10..200</a>
%F a(n) = A008290(n,10).
%F E.g.f.: exp(-x)/(1-x)*(x^10/10!). [_Zerinvary Lajos_, Apr 03 2009]
%F O.g.f.: (1/10!)*Sum_{k>=10} k!*x^k/(1 + x)^(k+1). - _Ilya Gutkovskiy_, Apr 15 2017
%p a:=n->sum(n!*sum((-1)^k/(k-9)!, j=0..n), k=9..n): seq(-a(n)/10!, n=9..27);
%p restart: G(x):=exp(-x)/(1-x)*(x^10/10!): 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=10..26); # _Zerinvary Lajos_, Apr 03 2009
%t With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^10/10!, {x, 0, nn}], x]Range[0, nn]!, 10]] (* _Vincenzo Librandi_, Feb 19 2014 *)
%o (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^9/9!)) ) \\ _Joerg Arndt_, Feb 19 2014
%Y Cf. A008290, A008291, A170942.
%K nonn
%O 10,3
%A _Zerinvary Lajos_, May 25 2007
%E Changed offset from 0 to 10 by _Vincenzo Librandi_, Feb 19 2014
%E Edited by _Joerg Arndt_, Feb 19 2014
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