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 A165172 #8 Apr 25 2023 15:22:12
%S A165172 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A165172 5489240266380,214080370358400,8349134442792000,325616243222649600,
%U A165172 12699033483880036800,495262305800992828800,19315229923495904673600
%N A165172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.
%C A165172 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A165172 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165172 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, -741).
%F A165172 G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
%F A165172 a(n) = -741*a(n-8) + 38*Sum_{k=1..7} a(n-k). - _Wesley Ivan Hurt_, Apr 25 2023
%K A165172 nonn
%O A165172 0,2
%A A165172 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009