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%I #19 Mar 21 2023 05:15:42
%S 9,16,23,30,37,44,53,60,67,74,83,90,99,106,113,118,127,134,143,150,
%T 159,164,173,180,189,194,203,208,217,224,235,240,249,254,263,268,279,
%U 284,293,298,309,314,325,330,339,342,353,358,369,374,385,388,399,404,415
%N Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_8.
%H I. Reiten, <a href="https://www.ams.org/journals/notices/199705/reiten.pdf">Dynkin diagrams and the representation theory of algebras</a>, Notices of the AMS, Vol. 44, No 5 (1997) 546-556. [<a href="http://www.ams.org/mathscinet-getitem?mr=1444112">MR1444112</a>]
%F a(n) = 7*(n+1) + 2*A087866(n).
%F G.f.: (7/(1-x)^2) + 2*(1-x^15)/((1-x^6)*(1-x^10)*(1-x)).
%t CoefficientList[ Series[ (9-2x+9x^3-2x^4+9x^5-2x^7+9x^8) / (1-2x+x^2+x^3-2x^4+2x^5-2x^6+x^7+x^8-2x^9+x^10), {x, 0, 54}], x] (* _Jean-François Alcover_, Dec 02 2011 *)
%Y Cf. A087866, A091572, A091573, A091574, A091575, A091576, A091577.
%K easy,nonn
%O 0,1
%A _Paul Boddington_, Jan 22 2004
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