A342587 Triangle, read by rows: T(n,k) is the number of labeled order relations on n nodes in which the longest chain has k nodes (n>=1, 1<=k<=n).

1, 1, 2, 1, 12, 6, 1, 86, 108, 24, 1, 840, 2310, 960, 120, 1, 11642, 65700, 42960, 9000, 720, 1, 227892, 2583126, 2510760, 712320, 90720, 5040, 1, 6285806, 142259628, 199357704, 71310960, 11481120, 987840, 40320, 1, 243593040, 11012710470, 21774014640, 9501062760, 1781015040

Offset: 1

Author

R. J. Mathar and Brendan McKay, Mar 16 2021

Keywords

• nonn
• tabl
• nice

Comments

Corrects Comtet's table for k=4 and 5 in row n=8.

Examples

			Triangle T(n,k) (with n >= 1 and 1 <= k <= n) begins as follows:
  1;
  1,      2;
  1,     12,       6;
  1,     86,     108,      24;
  1,    840,    2310,     960,    120;
  1,  11642,   65700,   42960,   9000,   720;
  1, 227892, 2583126, 2510760, 712320, 90720, 5040;
  ...
		

Links

• Brendan McKay, Table of T(n,k) for n = 1..13
• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.

Crossrefs

Cf. A000142 (diagonal), A001035 (row sums), A055531 (k=2), A055532 (k=3), A055533 (subdiagonal), A055534 (subdiagonal), A081064, A342501 (connected).