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%I #8 Apr 10 2022 16:36:16
%S 1,16,93,340,950,2226,4606,8688,15255,25300,40051,60996,89908,128870,
%T 180300,246976,332061,439128,572185,735700,934626,1174426,1461098,
%U 1801200,2201875,2670876,3216591,3848068,4575040,5407950,6357976
%N a(n) = (n+1)^2*(n+2)*(5*n^2 + 15*n + 12)/24.
%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. 231, # 37).
%F G.f.: (1 + 10*x + 12*x^2 + 2*x^3)/(1-x)^6.
%p a:=n->(n+1)^2*(n+2)*(5*n^2+15*n+12)/24: seq(a(n),n=0..36);
%t Table[(n+1)^2(n+2)(5n^2+15n+12)/24,{n,0,30}] (* _Harvey P. Dale_, Apr 10 2022 *)
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 17 2005
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