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%I #9 Jul 23 2018 02:49:33
%S 1,1,0,1,0,0,1,0,0,1,1,0,0,0,3,1,0,0,0,3,6,1,0,0,0,1,15,10,1,0,0,0,1,
%T 20,45,15,1,0,0,0,0,19,120,105,21,1,0,0,0,0,18,220,445,210,28,1
%N Let L_k(n) denote the number of elements of rank k in the free distributive lattice on n generators. Sequence gives irregular triangle, read by rows, showing coefficients when L_k(n) is expressed as a linear combination of binomial(n,i) for 0 <= i <= k-1.
%H George Markowsky, <a href="https://doi.org/10.1016/0012-365X(80)90156-9">The level polynomials of the free distributive lattices</a>, Discrete Mathematics 29.3 (1980): 275-285. Gives rows 0 through 16.
%e Triangle begins:
%e 1
%e 1
%e 0 1
%e 0 0 1
%e 0 0 1 1
%e 0 0 0 3 1
%e 0 0 0 3 6 1
%e 0 0 0 1 15 10 1
%e 0 0 0 1 20 45 15 1
%e 0 0 0 0 19 120 105 21 1
%e 0 0 0 0 18 220 445 210 28 1
%e ...
%K nonn,tabf,more
%O 0,15
%A _N. J. A. Sloane_, Jul 22 2018
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