cp's OEIS Frontend

A129255 Permutations with exactly 12 fixed points.

%I A129255 #22 Jul 06 2023 05:19:27
%S A129255 1,0,91,910,16380,272272,4919460,93419352,1868513010,39238479280,
%T A129255 863247190806,19854684036460,476512419579196,11912810484279600,
%U A129255 309733072600927300,8362792960207653240,234158202885844712475
%N A129255 Permutations with exactly 12 fixed points.
%H A129255 Vincenzo Librandi, <a href="/A129255/b129255.txt">Table of n, a(n) for n = 12..200</a>
%H A129255 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for sequences related to permutations with fixed points</a>
%F A129255 E.g.f.: exp(-x)/(1-x)*(x^12/12!). [_Zerinvary Lajos_, Apr 03 2009]
%F A129255 O.g.f.: (1/12!)*Sum_{k>=12} k!*x^k/(1 + x)^(k+1). - _Ilya Gutkovskiy_, Apr 15 2017
%p A129255 a:=n->sum(n!*sum((-1)^k/(k-11)!, j=0..n), k=11..n): seq(-a(n)/12!, n=11..28);
%p A129255 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 A129255 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 A129255 (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^12/12!)) ) \\ _Joerg Arndt_, Feb 19 2014
%Y A129255 Column k=12 of A008290.
%Y A129255 Cf. A008291, A170942.
%K A129255 nonn
%O A129255 12,3
%A A129255 _Zerinvary Lajos_, May 25 2007
%E A129255 Changed offset from 0 to 12 by _Vincenzo Librandi_, Feb 19 2014
%E A129255 Edited by _Joerg Arndt_, Feb 19 2014