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%I #12 Apr 23 2020 10:01:58
%S 1,22,182,915,3388,10192,26376,60894,128535,252406,467038,822185,
%T 1387386,2257360,3558304,5455164,8159949,11941158,17134390,24154207,
%U 33507320,45807168,61789960,82332250,108470115,141420006,182601342
%N a(n) = (n+1)(n+2)^2*(n+3)(2n+3)(5n^2 + 19n + 20)/720.
%C Kekulé numbers for certain benzenoids.
%H Colin Barker, <a href="/A107969/b107969.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. 230).
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-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)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
%F (End)
%p a:=n->(1/720)*(n+1)*(n+2)^2*(n+3)*(2*n+3)*(5*n^2+19*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)^8 + O(x^30)) \\ _Colin Barker_, Apr 22 2020
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 12 2005
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