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

0,5

Links

Table of n, a(n) for n=0..27.

John Tyler Rascoe, Python program.

Example

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}}.

Prog

(Python) # see links

Crossrefs

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

Sequence in context: A373398 A075440 A137470 * A112492 A210574 A353532

Adjacent sequences: A379709 A379710 A379711 * A379713 A379714 A379715

Keyword

nonn,tabl,more,hard

Author

John Tyler Rascoe, Dec 30 2024

Status

approved