A379712 Triangle read by rows: T(n,k) is the number of nonempty labeled antichains of subsets of [n] such that the largest subset is of size k.

1, 1, 1, 1, 3, 1, 1, 7, 10, 1, 1, 15, 97, 53, 1, 1, 31, 1418, 5443, 686, 1, 1, 63, 40005, 3701128, 4043864, 43291, 1

Offset: 0

Author

John Tyler Rascoe, Dec 30 2024

Keywords

• nonn
• tabl
• more
• hard

Examples

			Triangle begins:
   k=0   1     2     3    4  5
 n=0 1;
 n=1 1,  1;
 n=2 1,  3,    1;
 n=3 1,  7,   10,    1;
 n=4 1, 15,   97,   53,   1;
 n=5 1, 31, 1418, 5443, 686, 1;
 ...
T(3,0) =  1: {{}}.
T(3,1) =  7: {{1}}, {{2}}, {{3}}, {{1},{2}}, {{1},{3}}, {{2},{3}}, {{1},{2},{3}}.
T(3,2) = 10: {{1,2}}, {{1,3}}, {{2,3}}, {{1},{23}}, {{2},{13}}, {{3},{12}}, {{12},{13}}, {{12},{23}}, {{13},{23}}, {{12},{13},{23}}.
T(3,3) =  1: {{1,2,3}}.
		

Links

• John Tyler Rascoe, Python program.

Crossrefs

Cf. (column k=1) A000225, A000372, (row sums) A014466, A327806, (column k=2) A379706.

Programs

Python

# see links