A342500 - OEIS

A342500

T(n,k) is the number of connected unlabeled posets with n elements and rank k: triangle read by rows.

1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 10, 24, 9, 1, 0, 27, 123, 73, 14, 1, 0, 88, 734, 638, 169, 20, 1, 0, 328, 5184, 6460, 2178, 334, 27, 1, 0, 1460, 44518, 78385, 32468, 5880, 594, 35, 1, 0, 7799, 472859, 1164966, 581533, 118933, 13605, 979, 44, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

This is a variant of A263859 admitting only connected posets.

LINKS

Table of n, a(n) for n=1..55.

Index entries for sequences related to posets

R. J. Mathar, Poset Illustrations

FORMULA

T(n,0) = 0 for k>0; due to the connectivity constraint.

T(n,n-1) = 1; the poset with elements in a single chain.

EXAMPLE

The table starts in row n=1 shows ranks k>=0:

1: 1

2: 0 1

3: 0 2 1

4: 0 4 5 1

5: 0 10 24 9 1

6: 0 27 123 73 14 1

7: 0 88 734 638 169 20 1

8: 0 328 5184 6460 2178 334 27 1

9: 0 1460 44518 78385 32468 5880 594 35 1

10: 0 7799 472859 1164966 581533 118933 13605 979 44 1

CROSSREFS

Cf. A000608 (row sums), A007776 (rank 1), A263859, A000096 (subdiagonal), A342501 (labeled).

Sequence in context: A164994 A269952 A361954 * A247268 A266867 A151852

Adjacent sequences: A342497 A342498 A342499 * A342501 A342502 A342503

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, Mar 14 2021

STATUS

approved