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 A172501 #19 Aug 29 2022 04:41:17
%S A172501 1,54,1620,35640,641520,10007712,140107968,1801388160,21616657920,
%T A172501 244988789760,2645878929408,27420927086592,274209270865920,
%U A172501 2657720625315840,25058508752977920,230538280527396864,2074844524746571776,18307451688940339200,158664581304149606400
%N A172501 a(n) = binomial(n+8,8)*6^n.
%C A172501 With a different offset, number of n-permutations (n>=8) of 7 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's.
%H A172501 Vincenzo Librandi, <a href="/A172501/b172501.txt">Table of n, a(n) for n = 0..400</a>
%H A172501 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (54,-1296,18144,-163296,979776,-3919104,10077696,-15116544,10077696).
%F A172501 From _Colin Barker_, Jul 24 2017: (Start)
%F A172501 G.f.: 1 / (1 - 6*x)^9.
%F A172501 a(n) = (2^(-7 + n)*3^(-2 + n)*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(6 + n)*(7 + n)*(8 + n)) / 35.
%F A172501 (End)
%F A172501 From _Amiram Eldar_, Aug 29 2022: (Start)
%F A172501 Sum_{n>=0} 1/a(n) = 4785948/7 - 3750000*log(6/5).
%F A172501 Sum_{n>=0} (-1)^n/a(n) = 39530064*log(7/6) - 213275484/35. (End)
%t A172501 Table[Binomial[n + 8, 8]*6^n, {n, 0, 20}]
%o A172501 (Magma) [6^n* Binomial(n+8, 8): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%o A172501 (PARI) Vec(1 / (1 - 6*x)^9 + O(x^30)) \\ _Colin Barker_, Jul 24 2017
%Y A172501 Cf. A081136, A081144, A139626, A036084, A050988, A141407.
%K A172501 nonn,easy
%O A172501 0,2
%A A172501 _Zerinvary Lajos_, Feb 05 2010