A361957 Triangle read by rows: T(n,k) is the number of unlabeled tiered posets with n elements and height k.

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 5, 3, 1, 0, 1, 12, 10, 4, 1, 0, 1, 35, 35, 16, 5, 1, 0, 1, 108, 149, 66, 23, 6, 1, 0, 1, 393, 755, 327, 106, 31, 7, 1, 0, 1, 1666, 4736, 1936, 566, 156, 40, 8, 1, 0, 1, 8543, 37394, 14130, 3578, 878, 217, 50, 9, 1

Offset: 0

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, 1,    1;
  0, 1,    2,    1;
  0, 1,    5,    3,    1;
  0, 1,   12,   10,    4,   1;
  0, 1,   35,   35,   16,   5,   1;
  0, 1,  108,  149,   66,  23,   6,  1;
  0, 1,  393,  755,  327, 106,  31,  7, 1;
  0, 1, 1666, 4736, 1936, 566, 156, 40, 8, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..860 (rows 0..40).
• Andrew Howroyd, PARI Program, Apr 2023.

Crossrefs

Row sums are A361912.

Column k=2 is A055192.

The labeled version is A361956.

Cf. A361953, A361958 (connected).

Programs

PARI

\\ See link for program code.
{ my(A=A361957tabl(9)); for(i=1, #A, print(A[i, 1..i])) }