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%I #25 Jul 06 2023 05:27:15
%S 1,0,28,168,1890,20328,244860,3181464,44543499,668147480,10690367688,
%T 181736238320,3271252308324,62153793831024,1243075876659240,
%U 26104593409789776,574301055015449685,13208924265355241808
%N Permutations with exactly 6 fixed points.
%H Vincenzo Librandi, <a href="/A129136/b129136.txt">Table of n, a(n) for n = 6..200</a>
%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000022">The number of fixed points of a permutation</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for sequences related to permutations with fixed points</a>
%F a(n) = A008290(n,6).
%F E.g.f.: exp(-x)/(1-x)*(x^6/6!). [_Zerinvary Lajos_, Apr 03 2009]
%F O.g.f.: (1/6!)*Sum_{k>=6} k!*x^k/(1 + x)^(k+1). - _Ilya Gutkovskiy_, Apr 15 2017
%F D-finite with recurrence +(-n+6)*a(n) +n*(n-7)*a(n-1) +n*(n-1)*a(n-2)=0. - _R. J. Mathar_, Jul 06 2023
%p a:=n->sum(n!*sum((-1)^k/(k-5)!, j=0..n), k=5..n): seq(-a(n)/6!, n=5..24);
%p 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
%t 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 *)
%o (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^6/6!)) ) \\ _Joerg Arndt_, Feb 19 2014
%Y Cf. A008290, A008291, A170942.
%K nonn
%O 6,3
%A _Zerinvary Lajos_, May 25 2007
%E Changed offset from 0 to 6 by _Vincenzo Librandi_, Feb 19 2014
%E Edited by _Joerg Arndt_, Feb 19 2014
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