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%I #19 May 31 2022 03:20:22
%S 20,432,3024,12800,40500,105840,241472,497664,947700,1694000,2874960,
%T 4672512,7320404,11113200,16416000,23674880,33428052,46317744,
%U 63102800,84672000,112058100,146452592,189221184,241920000,306312500,384387120
%N a(n) = (n+1)^3*(n+2)^2*(n+5).
%C Kekulé numbers for certain benzenoids.
%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 310).
%H Vincenzo Librandi, <a href="/A109116/b109116.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: 4(5 + 73x + 105x^2 + x^3 - 4x^4)/(1-x)^7.
%F From _Amiram Eldar_, May 31 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 8473/6912 - 43*Pi^2/288 + zeta(3)/4.
%F Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/9 + 3*zeta(3)/16 - 11*Pi^2/576 - 8441/6912. (End)
%p a:=n->(n+1)^3*(n+2)^2*(n+5): seq(a(n),n=0..30);
%t Table[(n+1)^3 (n+2)^2 (n+5),{n,0,30}] (* _Harvey P. Dale_, Sep 24 2011 *)
%o (Magma) [(n+1)^3*(n+2)^2*(n+5): n in [0..30]]; // _Vincenzo Librandi_, Sep 25 2011
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Jun 19 2005
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