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%I #11 Apr 23 2020 10:01:36
%S 1,23,205,1120,4508,14700,41076,101970,230505,482911,949949,1772134,
%T 3159520,5416880,8975184,14430348,22590297,34531455,51665845,75820052,
%U 109327372,155134540,216924500,299256750,407726865,549146871,731748213
%N a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(5n^2 + 21n + 20)/2880.
%C Kekulé numbers for certain benzenoids.
%H Colin Barker, <a href="/A107956/b107956.txt">Table of n, a(n) for n = 0..1000</a>
%H S. J. Cyvin and I. Gutman, <a href="https://doi.org/10.1007/978-3-662-00892-8">Kekulé structures in benzenoid hydrocarbons</a>, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F From _Colin Barker_, Apr 22 2020: (Start)
%F G.f.: (1 + 14*x + 34*x^2 + 19*x^3 + 2*x^4) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
%F (End)
%p a:=n->(1/2880)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(5*n^2+21*n+20): seq(a(n),n=0..30);
%o (PARI) Vec((1 + 14*x + 34*x^2 + 19*x^3 + 2*x^4) / (1 - x)^9 + O(x^30)) \\ _Colin Barker_, Apr 22 2020
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 12 2005