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 A051689 #14 Sep 08 2022 08:44:59
%S A051689 1,13,234,5382,150696,4972968,188972784,8125829712,390039826176,
%T A051689 20672110787328,1198982425665024,75535892816896512,
%U A051689 5136440711548962816,374960171943074285568,29246893411559794274304
%N A051689 a(n) = (5*n+8)(!^5)/8(!^5), related to A034300 ((5*n+3)(!^5) quintic, or 5-factorials).
%C A051689 Row m=8 of the array A(6; m,n) := ((5*n+m)(!^5))/m(!^5), m >= 0, n >= 0.
%H A051689 G. C. Greubel, <a href="/A051689/b051689.txt">Table of n, a(n) for n = 0..352</a>
%F A051689 a(n) = ((5*n+8)(!^5))/8(!^5) = A034300(n+2)/8.
%F A051689 E.g.f.: 1/(1-5*x)^(13/5).
%t A051689 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 12, 5!, 5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A051689 With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(13/5), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)
%o A051689 (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-5*x)^(13/5))) \\ _G. C. Greubel_, Aug 15 2018
%o A051689 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^(13/5))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018
%Y A051689 Cf. A052562, A008548(n+1), A034323(n+1), A034300(n+1), A034301(n+1), A034325(n+1), A051687-A051691 (rows m=0..10).
%K A051689 easy,nonn
%O A051689 0,2
%A A051689 _Wolfdieter Lang_