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 A028200 #35 Feb 13 2025 07:57:57
%S A028200 1,30,565,8550,113701,1388310,15958405,175419750,1863406501,
%T A028200 19269697590,195034120645,1939826329350,19018419228901,
%U A028200 184245490086870,1767124523521285,16805853434269350,158682246543588901,1489103597614860150,13900428943759584325
%N A028200 Expansion of 1/((1-6x)*(1-7x)*(1-8x)*(1-9x)).
%H A028200 Matthew House, <a href="/A028200/b028200.txt">Table of n, a(n) for n = 0..1040</a>
%H A028200 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (30,-335,1650,-3024).
%F A028200 If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,6), (n >= 3). [_Milan Janjic_, Apr 26 2009]
%F A028200 a(n) = 17*a(n-1) - 72*a(n-2) + 7^(n+1) - 6^(n+1), a(0)=1, a(1)=30. - _Vincenzo Librandi_, Mar 11 2011
%F A028200 a(n) = (9^(n+3) - 3*8^(n+3) + 3*7^(n+3) - 6^(n+3))/6. [_Yahia Kahloune_, Jun 12 2013]
%F A028200 a(n) = 30*a(n-1) - 335*a(n-2) + 1650*a(n-3) - 3024*a(n-4). - _Matthew House_, Feb 11 2017
%t A028200 CoefficientList[Series[ 1/((1-6x)(1-7x)(1-8x)(1-9x)), {x, 0, 20} ], x]
%t A028200 LinearRecurrence[{30,-335,1650,-3024},{1,30,565,8550},20] (* _Harvey P. Dale_, Mar 27 2023 *)
%o A028200 (PARI) Vec(1/((1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) + O(x^30)) \\ _Michel Marcus_, Feb 12 2017
%Y A028200 Cf. A000453, A025211, A028025, A003468, A028165, A016109, A016075, A016094.
%K A028200 nonn
%O A028200 0,2
%A A028200 _N. J. A. Sloane_