This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108681 #16 Jul 22 2022 09:38:48
%S A108681 1,15,98,420,1386,3822,9240,20196,40755,77077,138138,236600,389844,
%T A108681 621180,961248,1449624,2136645,3085467,4374370,6099324,8376830,
%U A108681 11347050,15177240,20065500,26244855,33987681,43610490,55479088,70014120,87697016,109076352,134774640
%N A108681 a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(n+5)*(2*n+3)/720.
%C A108681 Kekulé numbers for certain benzenoids.
%D A108681 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 232, # 4).
%H A108681 <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 A108681 G.f.: (1+x)*(1+6*x)/(1-x)^8.
%F A108681 From _Amiram Eldar_, Jun 02 2022: (Start)
%F A108681 Sum_{n>=0} 1/a(n) = 20*Pi^2 - 3072*log(2)/7 + 4531/42.
%F A108681 Sum_{n>=0} (-1)^n/a(n) = 768*Pi/7 - 10*Pi^2 - 256*log(2)/7 - 9227/42. (End)
%F A108681 a(n) = A027818(n)+A027818(n-1). - _R. J. Mathar_, Jul 22 2022
%p A108681 G:=factor(sum(a(n)*z^n,n=0..infinity)); series(G,z=0,37);
%t A108681 Table[(n+1)(n+2)^2(n+3)(n+4)(n+5)(2n+3)/720,{n,0,30}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,15,98,420,1386,3822,9240,20196},30] (* _Harvey P. Dale_, Sep 23 2017 *)
%K A108681 nonn,easy
%O A108681 0,2
%A A108681 _Emeric Deutsch_, Jun 18 2005