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%I #12 Apr 26 2015 12:04:46
%S 1,1,1,1,3,1,1,4,4,1,1,6,8,6,1,1,7,14,14,7,1,1,9,21,28,21,9,1,1,10,30,
%T 49,49,30,10,1,1,12,40,79,98,79,40,12,1,1,13,52,119,177,177,119,52,13,
%U 1,1,15,65,171,296,354,296,171,65,15,1,1,16,80
%N Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(n,1)=T(n,n-1)=[ 3n/2 ] for n >= 1; T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=k<=n-2, n >= 4.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) for i=0, j >= 0 and even and for j=0, i >= 0 and even.
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 4, 4, 1;
%e 1, 6, 8, 6, 1;
%e 1, 7, 14, 14, 7, 1;
%e 1, 9, 21, 28, 21, 9, 1;
%e 1, 10, 30, 49, 49, 30, 10, 1;
%e 1, 12, 40, 79, 98, 79, 40, 12, 1;
%e 1, 13, 52, 119, 177, 177, 119, 52, 13, 1;
%e 1, 15, 65, 171, 296, 354, 296, 171, 65, 15, 1;
%K nonn,tabl,easy
%O 1,5
%A _Clark Kimberling_
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