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 A265055 #37 Sep 08 2022 08:46:14
%S A265055 1,4,9,16,25,37,53,74,101,135,179,237,313,411,537,700,912,1188,1546,
%T A265055 2009,2608,3385,4394,5703,7399,9596,12444,16138,20929,27140,35190,
%U A265055 45625,59155,76699,99445,128932,167158,216717,280972,364279,472282,612300,793827,1029174,1334298
%N A265055 Expansion of b(2)*b(4)*b(6)/(x^8-x^4-x+1), where b(k) = (1-x^k)/(1-x).
%C A265055 This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_1 - see Tables 7.6, 7.7 and 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Tables 5 and 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).
%H A265055 Colin Barker, <a href="/A265055/b265055.txt">Table of n, a(n) for n = 0..1000</a>
%H A265055 Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="https://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.
%H A265055 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 17.supp01 (2010): 169-215.
%H A265055 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,0,0,-1).
%F A265055 G.f.: (1 + x^2)*(1 - x + x^2)*(1 + x + x^2)*(1 + x)^3/((1 - x)*(1 - x^4 - x^5 - x^6 - x^7)). [_Bruno Berselli_, Dec 28 2015]
%t A265055 Join[{1, 4}, LinearRecurrence[{1, 0, 0, 1, 0, 0, 0, -1}, {9, 16, 25, 37, 53, 74, 101, 135}, 50]] (* _Jean-François Alcover_, Jan 08 2019 *)
%o A265055 (Magma) /* By definition: */ m:=50; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(4)*b(6)/(x^8-x^4-x+1))); // _Bruno Berselli_, Dec 28 2015
%Y A265055 For diagrams QL4_1 - QL4_22 see: A265055, A266333, A266334, A266335, A266336, A266338, A266339, A266340, A266370, A266371, A266372, A266373, A266374, A266375, A266376, A266367, A266353, A266355, A266354, A264079, A266337, A162740 respectively.
%K A265055 nonn,easy
%O A265055 0,2
%A A265055 _N. J. A. Sloane_, Dec 27 2015