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%I #21 Sep 11 2021 19:23:08
%S 0,1,0,0,2,4,0,0,0,3,24,26,0,0,0,0,8,98,284,214,0,0,0,0,0,19,374,1922,
%T 3496,2030,0,0,0,0,0,0,44,1342,10620,33398,44674,21174,0,0,0,0,0,0,0,
%U 111,4596,51904,245684,554500,589092,236410
%N Irregular triangle read by rows: T(n,k) (1 <= k <= 2*n) = number of n X k Baxter matrices in which all row sums are 2.
%H Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/baxter-matrices.pdf">Baxter matrices</a>, Preprint, Sep 05 2021.
%e The T(4,5)=8 matrices of size 4 X 5 are
%e .
%e 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1
%e 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0
%e 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0
%e 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1
%e .
%e 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0
%e 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0
%e 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0
%e 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1
%Y Cf. A347678, A347736 (superdiagonal).
%K nonn,tabf,more
%O 1,5
%A _N. J. A. Sloane_, Sep 10 2021