%I #17 Sep 08 2022 08:46:15
%S 1,4,10,21,41,78,145,266,485,882,1601,2902,5256,9516,17226,31180,
%T 56435,102143,184868,334588,605559,1095976,1983558,3589950,6497282,
%U 11759123,21282277,38517777,69711482,126167473,228344464,413269701,747957021,1353691555,2449981446
%N Expansion of b(2)*b(6)*b(10)/(1 - x - x^2 - x^4 - x^5 + x^11 + x^12 + x^14), where b(k) = (1-x^k)/(1-x).
%C This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_19 - see Table 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Table 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).
%H Colin Barker, <a href="/A266354/b266354.txt">Table of n, a(n) for n = 0..1000</a>
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="http://arxiv.org/abs/0906.1596">The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, arXiv:0906.1596 [math.RT], 2009, page 31.
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="http://dx.doi.org/10.1142/S1402925110000842">The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, Journal of Nonlinear Mathematical Physics, Volume 17, Supplement 1 (2010), page 186.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,1,-1,1,0,-1,1,-1).
%F G.f.: (1 + x)^3*(1 - x + x^2)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)/((1 - x)*(1 - x - x^2 - x^4 - x^6 - x^7 - x^9)).
%t CoefficientList[Series[(1 + x)^3 (1 - x + x^2) (1 + x + x^2) (1 - x + x^2 - x^3 + x^4)/((1 - x) (1 - x - x^2 - x^4 - x^6 - x^7 - x^9)), {x, 0, 40}], x]
%o (Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(6)*b(10)/(1-x-x^2-x^4-x^5+x^11+x^12+x^14)));
%Y Cf. similar sequences listed in A265055.
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Dec 28 2015