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 A165881 #19 Sep 08 2022 08:45:48
%S A165881 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A165881 209379250944,3768826516821,67838877299700,1221099791339367,
%U A165881 21979796243114412,395636332358163924,7121453982124831776
%N A165881 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165881 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A165881 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165881 G. C. Greubel, <a href="/A165881/b165881.txt">Table of n, a(n) for n = 0..500</a>
%H A165881 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (17,17,17,17,17,17,17,17,17,-153).
%F A165881 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)/(153*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
%p A165881 seq(coeff(series((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 24 2019
%t A165881 CoefficientList[Series[(1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), {t, 0, 20}], t] (* _G. C. Greubel_, Apr 17 2016 *)
%t A165881 coxG[{10,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 23 2017 *)
%o A165881 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)) \\ _G. C. Greubel_, Sep 24 2019
%o A165881 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11) )); // _G. C. Greubel_, Sep 24 2019
%o A165881 (Sage)
%o A165881 def A163878_list(prec):
%o A165881 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165881 return P((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)).list()
%o A165881 A163878_list(20) # _G. C. Greubel_, Sep 24 2019
%o A165881 (GAP) a:=[19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821];; for n in [11..20] do a[n]:=17*Sum([1..9], j-> a[n-j]) -153*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 24 2019
%Y A165881 Cf. A154638, A170738.
%K A165881 nonn
%O A165881 0,2
%A A165881 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009