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 A165880 #19 Sep 08 2022 08:45:48
%S A165880 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A165880 125563633938,2134581776793,36287890202880,616894133404896,
%U A165880 10487200267134144,178282404528545952,3030800876768794752,51523614901389241440
%N A165880 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165880 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A165880 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165880 G. C. Greubel, <a href="/A165880/b165880.txt">Table of n, a(n) for n = 0..500</a>
%H A165880 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (16,16,16,16,16,16,16,16,16,-136).
%F A165880 G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%p A165880 seq(coeff(series((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 24 2019
%t A165880 CoefficientList[Series[(1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11), {t, 0, 20}], t] (* _G. C. Greubel_, Apr 17 2016 *)
%t A165880 coxG[{10,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 04 2017 *)
%o A165880 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11)) \\ _G. C. Greubel_, Sep 24 2019
%o A165880 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11) )); // _G. C. Greubel_, Sep 24 2019
%o A165880 (Sage)
%o A165880 def A165880_list(prec):
%o A165880 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165880 return P((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11)).list()
%o A165880 A165880_list(20) # _G. C. Greubel_, Sep 24 2019
%o A165880 (GAP) a:=[18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776793];; for n in [11..20] do a[n]:=16*Sum([1..9], j-> a[n-j]) -136*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 24 2019
%Y A165880 Cf. A154638, A170737.
%K A165880 nonn
%O A165880 0,2
%A A165880 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009