A263859 Triangle read by rows: T(n,k) (n>=1, k>=0) is the number of posets with n elements and rank k (or depth k+1).

1, 1, 1, 1, 3, 1, 1, 8, 6, 1, 1, 20, 31, 10, 1, 1, 55, 162, 84, 15, 1, 1, 163, 940, 734, 185, 21, 1, 1, 556, 6372, 7305, 2380, 356, 28, 1, 1, 2222, 52336, 86683, 35070, 6259, 623, 36, 1, 1, 10765, 534741, 1261371, 619489, 125597, 14258, 1016, 45, 1

Offset: 1

Author

Christian Stump, Oct 28 2015

Keywords

• nonn
• tabl

Comments

Row sums give A000112, n >= 1.

The rank of a poset is the number of cover relations in a maximal chain.

Examples

			Triangle begins:
1,
1,1,
1,3,1,
1,8,6,1,
1,20,31,10,1,
1,55,162,84,15,1,
1,163,940,734,185,21,1,
1,556,6372,7305,2380,356,28,1,
1,2222,52336,86683,35070,6259,623,36,1,
1,10765,534741,1261371,619489,125597,14258,1016,45,1,
...
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..136
• G. Brinkmann and B. D. McKay, Posets on up to 16 Points [On Brendan McKay's home page]
• G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179.
• FindStat - Combinatorial Statistic Finder, The rank of the poset.
• Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 10 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Crossrefs

Cf. A000112 (row sums), A342500 (connected).

Extensions

More terms from Brinkmann-McKay (2002) added by N. J. A. Sloane, Mar 18 2017