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%I #13 Oct 07 2022 15:48:45
%S 1,0,1,1,0,1,0,4,0,1,4,0,9,0,1,0,25,0,16,0,1,25,0,81,0,25,0,1,0,196,0,
%T 196,0,36,0,1,196,0,784,0,400,0,49,0,1,0,1764,0,2304,0,729,0,64,0,1,
%U 1764,0,8100,0,5625,0,1225,0,81,0,1,0,17424,0,27225,0,12100,0
%N Triangle T(n,k) read by rows: Number of Dyck n-paths with midpoint at height k.
%F T(n,k) = A053121(n,k)^2.
%e Triangle T(n,k) begins:
%e 1
%e 0 1
%e 1 0 1
%e 0 4 0 1
%e 4 0 9 0 1
%e 0 25 0 16 0 1
%e 25 0 81 0 25 0 1
%e 0 196 0 196 0 36 0 1
%e 196 0 784 0 400 0 49 0 1
%e 0 1764 0 2304 0 729 0 64 0 1
%e 1764 0 8100 0 5625 0 1225 0 81 0 1
%e ...
%Y Row sums give A000108.
%Y T(2n,0) gives A001246.
%Y T(2n,2) gives A338727(n) for n>=1.
%Y Cf. A053121.
%K nonn,tabl
%O 0,8
%A _David Scambler_, Jun 14 2012
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