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A168789 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168789 #12 Nov 24 2016 16:17:57
%S A168789 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A168789 615093750000,9226406250000,138396093750000,2075941406250000,
%U A168789 31139121093750000,467086816406250000,7006302246093750000
%N A168789 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168789 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A168789 First disagreement at index 19: a(19) = 23646270080566406249880, A170735(19) = 23646270080566406250000. - _Klaus Brockhaus_, Mar 30 2011
%C A168789 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168789 G. C. Greubel, <a href="/A168789/b168789.txt">Table of n, a(n) for n = 0..500</a>
%H A168789 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A168789 G.f.: (t^19 + 2*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)/(105*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%t A168789 CoefficientList[Series[(t^19 + 2*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)/(105*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 15 2016 *)
%Y A168789 Cf. A170735 (G.f.: (1+x)/(1-15*x)).
%K A168789 nonn
%O A168789 0,2
%A A168789 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009