%I #19 May 31 2022 03:26:17
%S 1,90,2475,35035,321048,2159136,11511720,51210225,196994655,672567610,
%T 2078241165,5900460930,15576433600,38599672320,90491328576,
%U 201987412398,431582100885,886725689850,1758635878615,3378012822261,6302164837320,11448416980000,20294512875000
%N a(n) = (n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2n+5)*(2n+7)/7257600.
%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. 186, D(4,5,n)).
%H T. D. Noe, <a href="/A109124/b109124.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F G.f.: (1+x)(1 + 74x + 1156x^2 + 5749x^3 + 10064x^4 + 5749x^5 + 1156x^6 + 74x^7 + x^8)/(1-x)^15.
%F From _Amiram Eldar_, May 31 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 63344246/3 - 1940400*Pi^2 - 20160*Pi^4.
%F Sum_{n>=0} (-1)^n/a(n) = 18350080*Pi - 1222200*Pi^2 - 17640*Pi^4 - 131602646/3. (End)
%p a:=n->(n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2*n+5)*(2*n+7)/7257600: seq(a(n),n=0..23);
%t Table[((n+1)(n+2)^3 (n+3)^4 (n+4)^3 (n+5)(2n+5)(2n+7))/7257600,{n,0,30}] (* _Harvey P. Dale_, Sep 04 2020 *)
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 20 2005