%I
%S 1,1,1,1,2,1,1,1,1,1,1,2,2,2,1,1,3,2,2,3,1,1,4,5,4,5,4,1,1,5,9,5,5,9,
%T 5,1,1,6,14,14,10,14,14,6,1,1,7,20,28,14,14,28,20,7,1,1,8,27,48,42,28,
%U 42,48,27,8,1,1,9,35,75,90,42,42,90,75,35,9,1
%N Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=x unless x=0 or x=h.
%H R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</a>
%e Diagonals (beginning on row 0): {1}; {1,1}; {1,2,1}; {1,1,1,1}; {1,2,2,2,1}; ...
%Y T(n, n)=A002420, T(n, n+1)=A000108 (Catalan numbers).
%Y The following are all versions of (essentially) the same Catalan triangle: A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
%Y Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392, ...
%K nonn,tabl
%O 0,5
%A _Clark Kimberling_
