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%I #3 Mar 30 2012 18:58:43
%S 1,1,1,1,2,1,2,3,3,1,5,5,6,4,1,11,10,11,10,5,1,22,21,21,21,15,6,1,43,
%T 43,42,42,36,21,7,1,85,86,85,84,78,57,28,8,1,170,171,171,169,162,135,
%U 85,36,9,1,341,341,342,340,331,297,220,121,45,10,1,683,682,683,671,628,517
%N Number triangle related to a problem of Knuth.
%C In lower-triangular form, the columns are the binomial transforms of the sequences with g.f. x^(k-1)/(1-x^3). The first three columns are A024493, A024494, A024495.
%F T(n, 1) = A024493(n). T(n, k)=0, k>n, T(n, n)=1. T(n, k) = T(n-1, k-1)+T(n-1, k).
%e Rows are {1}, {1,1}, {1,2,1}, {2,3,3,1}, {5,5,6,4,1}, {11,10,11,10,5,1}...
%K easy,nonn,tabl
%O 1,5
%A _Paul Barry_, Feb 20 2003
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