A361958 Triangle read by rows: T(n,k) is the number of connected unlabeled tiered posets with n elements and height k.

1, 0, 1, 0, 2, 1, 0, 4, 3, 1, 0, 10, 10, 4, 1, 0, 27, 34, 16, 5, 1, 0, 88, 146, 66, 23, 6, 1, 0, 328, 739, 326, 106, 31, 7, 1, 0, 1460, 4671, 1932, 566, 156, 40, 8, 1, 0, 7799, 37088, 14104, 3577, 878, 217, 50, 9, 1, 0, 51196, 376524, 128652, 27563, 5740, 1276, 290, 61, 10, 1

Offset: 1

Author

Andrew Howroyd, Apr 03 2023

Keywords

• nonn
• tabl

Comments

A tiered poset is a partially ordered set in which every maximal chain has the same length.

Examples

			Triangle begins:
  1;
  0,    1;
  0,    2,    1;
  0,    4,    3,    1;
  0,   10,   10,    4,   1;
  0,   27,   34,   16,   5,   1;
  0,   88,  146,   66,  23,   6,  1;
  0,  328,  739,  326, 106,  31,  7, 1;
  0, 1460, 4671, 1932, 566, 156, 40, 8, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..820 (rows 1..40).

Crossrefs

Row sums are A361959.

Cf. A361954, A361957 (not necessarily connected).

Programs

PARI

\\ See PARI link in A361957 for program code.
{ my(A=A361958tabl(9)); for(i=1, #A, print(A[i, 1..i])) }

Formula

Column k is the inverse Euler transform of column k of A361957.