This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129153 #23 Jul 06 2023 05:25:19
%S A129153 1,0,45,330,4455,56628,795795,11930490,190900710,3245287760,
%T A129153 58415223438,1109889169740,22197783520770,466153453732680,
%U A129153 10255375982438730,235873647595600476,5660967542295146895,141524188557377590800
%N A129153 Rencontres numbers: permutations with exactly 8 fixed points.
%H A129153 Vincenzo Librandi, <a href="/A129153/b129153.txt">Table of n, a(n) for n = 8..200</a>
%H A129153 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for sequences related to permutations with fixed points</a>
%F A129153 a(n) = A008290(n,8).
%F A129153 E.g.f.: exp(-x)/(1-x)*(x^8/8!). [_Joerg Arndt_, Feb 19 2014]
%F A129153 O.g.f.: (1/8!)*Sum_{k>=8} k!*x^k/(1 + x)^(k+1). - _Ilya Gutkovskiy_, Apr 15 2017
%F A129153 D-finite with recurrence (-n+8)*a(n) +n*(n-9)*a(n-1) +n*(n-1)*a(n-2)=0. - _R. J. Mathar_, Jul 06 2023
%p A129153 a:= n-> -sum((n-1)!*sum((-1)^k/(k-7)!, j=0..n-1), k=7..n-1)/8!: seq(a(n), n=8..30);
%t A129153 With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^8/8!, {x, 0, nn}], x]Range[0, nn]!, 8]] (* _Vincenzo Librandi_, Feb 19 2014 *)
%o A129153 (PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^8/8!)) ) \\ _Joerg Arndt_, Feb 19 2014
%Y A129153 Column k=8 of A008290.
%Y A129153 Cf. A008291, A170942.
%K A129153 nonn
%O A129153 8,3
%A A129153 _Zerinvary Lajos_, May 25 2007
%E A129153 Changed offset from 0 to 8 by _Vincenzo Librandi_, Feb 19 2014