A065066 Triangle T(n,k) read by rows of partially ordered sets ("posets") with n unlabeled nodes and k maximal elements (0 <= k <= n).

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 7, 3, 1, 0, 16, 27, 15, 4, 1, 0, 63, 134, 88, 27, 5, 1, 0, 318, 814, 642, 221, 43, 6, 1, 0, 2045, 6258, 5828, 2319, 477, 64, 7, 1, 0, 16999, 60877, 66612, 30698, 7015, 931, 90, 8, 1, 0, 183231, 755323, 959941, 514525, 133610

Offset

0,8

Links

R. J. Mathar, Table of n, a(n) for n = 0..90

G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Tables 8, 10, 16, 20, 24, 28, 32, 36, 40...

FindStat - Combinatorial Statistic Finder, The number of minimal elements in a poset., The number of maximal elements of a poset.

Index entries for sequences related to posets

Formula

T(n+1, 1) = Sum_{i=0}^n T(n, i) = A000112(n).

Example

1,
0,1,
0,1,1,
0,2,2,1,
0,5,7,3,1,
0,16,27,15,4,1,
0,63,134,88,27,5,1,
0,318,814,642,221,43,6,1,
...

Crossrefs

Cf. A000112.

Sequence in context: A321960 A189233 A242153 * A266291 A064045 A258829

Adjacent sequences: A065063 A065064 A065065 * A065067 A065068 A065069

Keyword

nonn,tabl

Author

Jens Voß, Nov 07 2001

Extensions

Values beyond row 6 from R. J. Mathar, Mar 14 2021

Status

approved