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A168765 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168765 #17 Nov 24 2016 14:01:46
%S A168765 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A168765 5489240267160,214080370419240,8349134446350360,325616243407664040,
%U A168765 12699033492898897560,495262306223057004840,19315229942699223188760
%N A168765 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168765 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A168765 First disagreement at index 18: a(18) = 44684644873868033593028122380, A170759(18) = 44684644873868033593028123160. - _Klaus Brockhaus_, Mar 26 2011
%C A168765 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168765 G. C. Greubel, <a href="/A168765/b168765.txt">Table of n, a(n) for n = 0..500</a>
%H A168765 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
%F A168765 G.f.: (t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/(741*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
%t A168765 With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-38 t^Range[17]]+ 741t^18+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 31 2011 *)
%t A168765 CoefficientList[Series[(t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/(741*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 11 2016 *)
%Y A168765 Cf. A170759 (G.f.: (1+x)/(1-39*x)).
%K A168765 nonn,easy
%O A168765 0,2
%A A168765 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009