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 A051690 #18 Jan 04 2025 17:29:22
%S A051690 1,14,266,6384,185136,6294624,245490336,10801574784,529277164416,
%T A051690 28580966878464,1686277045829376,107921730933080064,
%U A051690 7446599434382524416,551048358144306806784,43532820293400237735936,3656756904645619969818624,325451364513460177313857536
%N A051690 a(n) = (5*n+9)(!^5)/9(!^5), related to A034301 ((5*n+2)(!^5) quintic, or 5-factorials).
%C A051690 Row m=9 of the array A(6; m,n) := ((5*n+m)(!^5))/m(!^5), m >= 0, n >= 0.
%H A051690 G. C. Greubel, <a href="/A051690/b051690.txt">Table of n, a(n) for n = 0..352</a>
%F A051690 a(n) = ((5*n+9)(!^5))/9(!^5) = A034301(n+2)/9.
%F A051690 E.g.f.: 1/(1-5*x)^(14/5).
%t A051690 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 13, 5!, 5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A051690 With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(14/5), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)
%o A051690 (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1-5*x)^(14/5))) \\ _G. C. Greubel_, Aug 15 2018
%o A051690 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^(14/5))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018
%Y A051690 Cf. A052562, A008548(n+1), A034323(n+1), A034300(n+1), A034301(n+1), A034325(n+1), A051687-A051691 (rows m=0..10).
%K A051690 easy,nonn
%O A051690 0,2
%A A051690 _Wolfdieter Lang_