A316836 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.

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, 20, 45, 15, 1, 0, 0, 0, 0, 19, 120, 105, 21, 1, 0, 0, 0, 0, 18, 220, 445, 210, 28, 1

Offset

0,15

Links

Table of n, a(n) for n=0..55.

George Markowsky, The level polynomials of the free distributive lattices, Discrete Mathematics 29.3 (1980): 275-285. Gives rows 0 through 16.

Example

Triangle begins:
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 20 45 15 1
0 0 0 0 19 120 105 21 1
0 0 0 0 18 220 445 210 28 1
...

Crossrefs

Sequence in context: A342557 A286131 A285631 * A058612 A099725 A285118

Adjacent sequences: A316833 A316834 A316835 * A316837 A316838 A316839

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Jul 22 2018

Status

approved