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

1,5

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 = 1..820 (rows 1..40).

Formula

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

Example

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;
  ...

Prog

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

Crossrefs

Row sums are A361959.

Cf. A361954, A361957 (not necessarily connected).

Sequence in context: A201701 A131667 A322080 * A334122 A086802 A092488

Adjacent sequences: A361955 A361956 A361957 * A361959 A361960 A361961

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 03 2023

Status

approved