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 A123349 #10 Nov 16 2019 07:30:10
%S A123349 1,1,1,1,2,1,1,3,5,1,1,4,14,10,1,1,5,30,46,17,1,1,6,55,146,117,26,1,1,
%T A123349 7,91,371,517,251,37,1,1,8,140,812,1742,1476,478,50,1,1,9,204,1596,
%U A123349 4878,6376,3614,834,65,1,1,10,285,2892,11934,22252,19490,7890,1361,82,1,1,11
%N A123349 Square array of Kekulé numbers for the mirror-symmetrical chevrons Ch(m,n), read by antidiagonals (m,n >= 0).
%C A123349 T(m,1)=A002522(m); T(m,2)=A123350(m); T(m,3)=A123351(m).
%D A123349 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see pp. 119-120).
%F A123349 T(m,n) = Sum_{i=0..n} binomial(m+i-1, i)^2.
%e A123349 T(1,1)=2 because Ch(1,1) consists of a single hexagon; it has 2 perfect matchings: {1,3,5} and {2,4,6}, the edges of the hexagon being labeled consecutively by 1,2,3,4,5,6.
%e A123349 Square array starts:
%e A123349 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A123349 1, 2, 3, 4, 5, 6, 7, 8, ...
%e A123349 1, 5, 14, 30, 55, 91, 140, 204, ...
%e A123349 1, 10, 46, 146, 371, 812, 1596, 2892, ...
%e A123349 1, 17, 117, 517, 1742, 4878, 11934, 26334, ...
%p A123349 T:=(m,n)->sum(binomial(m+i-1,i)^2,i=0..n): TT:=(m,n)->T(m-1,n-1): matrix(9,9,TT); # yields sequence in matrix form
%Y A123349 Cf. A002522, A123350, A123351.
%K A123349 nonn,tabl
%O A123349 0,5
%A A123349 _N. J. A. Sloane_, Oct 14 2006
%E A123349 Edited by _Emeric Deutsch_, Oct 27 2006, Oct 28 2006