A361956 Triangle read by rows: T(n,k) is the number of labeled tiered posets with n elements and height k.

1, 0, 1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 50, 36, 24, 0, 1, 510, 510, 240, 120, 0, 1, 7682, 10620, 4800, 1800, 720, 0, 1, 161406, 312606, 136920, 47040, 15120, 5040, 0, 1, 4747010, 13439076, 5630184, 1678320, 493920, 141120, 40320, 0, 1, 194342910, 821218110, 319384800, 83963880, 21137760, 5594400, 1451520, 362880

Offset

0,6

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..1325 (rows 0..50).

Example

Triangle begins:
  1;
  0, 1;
  0, 1,      2;
  0, 1,      6,      6;
  0, 1,     50,     36,     24;
  0, 1,    510,    510,    240,   120;
  0, 1,   7682,  10620,   4800,  1800,   720;
  0, 1, 161406, 312606, 136920, 47040, 15120, 5040;
  ...

Prog

(PARI)
S(M)={my(N=matrix(#M-1, #M-1, i, j, sum(k=1, i-j+1, (2^j-1)^k*M[i-j+1, k])/j!)); for(i=1, #N, for(j=1, i, N[i, j] -= sum(k=1, j-1, N[i-k, j-k]/k!))); N}
C(n)={my(M=matrix(n+1, n+1), R=M); M[1, 1]=R[1, 1]=1; for(h=1, n, M=S(M); for(i=h, n, R[i+1, h+1] = i!*vecsum(M[i-h+1, ]))); R}
{ my(A=C(7)); for(i=1, #A, print(A[i, 1..i])) }

Crossrefs

Row sums are A223911.

Column k=2 is A052332.

Main diagonal is A000142.

The unlabeled version is A361957.

Cf. A222864, A361951.

Sequence in context: A131689 A278075 A114329 * A241011 A220905 A353451

Adjacent sequences: A361953 A361954 A361955 * A361957 A361958 A361959

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 02 2023

Status

approved