%I
%S 1,16,100,399,1218,3108,6972,14190,26763,47476,80080,129493,202020,
%T 305592,450024,647292,911829,1260840,1714636,2296987,3035494,3961980,
%U 5112900,6529770,8259615,10355436,12876696,15889825,19468744,23695408
%N a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(19*n^2 + 47*n + 30)/720.
%C KekulĂ© numbers for certain benzenoids.
%D S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 231, # 41).
%F G.f.: (1 + 9*x + 9*x^2)/(1x)^7.
%p a:=n>(n+1)*(n+2)*(n+3)*(n+4)*(19*n^2+47*n+30)/720: seq(a(n),n=0..33);
%t Table[(n+1)(n+2)(n+3)(n+4)(19n^2+47n+30)/720,{n,0,40}] (* _Harvey P. Dale_, Mar 04 2011 *)
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 17 2005
