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 A107983 #9 Feb 27 2015 09:27:11
%S A107983 1,6,4,20,20,10,50,60,45,20,105,140,126,84,35,196,280,280,224,140,56,
%T A107983 336,504,540,480,360,216,84,540,840,945,900,750,540,315,120,825,1320,
%U A107983 1540,1540,1375,1100,770,440,165,1210,1980,2376,2464,2310,1980,1540
%N A107983 Triangle read by rows: T(n,k) = (k+1)(n+2)(n+3)(n-k+2)(n-k+1)/12 for 0<=k<=n.
%C A107983 Kekulé numbers for certain benzenoids. Column 0 yields A002415. Main diagonal yields A000292. Row sums yield A006542.
%C A107983 T(n,k) = number of Dyck (n+4)-paths with 4 peaks (UDs) and last descent of length k+1. For example, T(1,1)=4 counts UUDUDUDUDD, UDUUDUDUDD, UDUDUUDUDD, UDUDUDUUDD. - _David Callan_, Jun 26 2006
%D A107983 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 237, K{F(n,3,-l)}).
%e A107983 Triangle begins:
%e A107983 1;
%e A107983 6,4;
%e A107983 20,20,10;
%e A107983 50,60,45,20;
%p A107983 T:=proc(n,k) if k<=n then (k+1)*(n+2)*(n+3)*(n-k+2)*(n-k+1)/12 else 0 fi end: for n from 0 to 10 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
%t A107983 Flatten[Table[((k+1)(n+2)(n+3)(n-k+2)(n-k+1))/12,{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Aug 08 2013 *)
%Y A107983 Cf. A002415, A000292, A006542.
%K A107983 nonn,tabl
%O A107983 0,2
%A A107983 _Emeric Deutsch_, Jun 12 2005