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

0,9

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 0..860 (rows 0..40).

Andrew Howroyd, PARI Program, Apr 2023.

Example

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;
  ...

Prog

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

Crossrefs

Row sums are A361912.

Column k=2 is A055192.

The labeled version is A361956.

Cf. A361953, A361958 (connected).

Sequence in context: A119331 A351641 A291883 * A239145 A327127 A151824

Adjacent sequences: A361954 A361955 A361956 * A361958 A361959 A361960

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 03 2023

Status

approved