A379706 Number of nonempty labeled antichains of subsets of [n] such that the largest subset is of size 2.

0, 0, 1, 10, 97, 1418, 40005, 2350474, 286192257, 71213783154, 35883905262757, 36419649682704418, 74221659280476132145, 303193505953871645554778, 2480118046704094643352342117, 40601989176407026666590990389338, 1329877330167226219547875498464450945, 87134888326188320631048795061602782878050

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{i=0..n-2} binomial(n,i) * (2^binomial(n-i,2) - 1).

Example

a(2) = 1: {{1,2}}.
a(3) = 10: {{1,2}}, {{1,3}}, {{2,3}}, {{1,2},{3}}, {{1,3},{2}}, {{2,3},{1}}, {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}, {{1,2},{1,3},{2,3}}.

Prog

(Python)
from math import comb
def A379706(n): return sum(comb(n, i)*(2**comb(n-i, 2) - 1) for i in range(n-1))

Crossrefs

Cf. A000225, A000372, A036239, A126883, A379707, (column k=2 of A379712).

Sequence in context: A209262 A308523 A190985 * A044642 A363186 A264462

Adjacent sequences: A379703 A379704 A379705 * A379707 A379708 A379709

Keyword

nonn,easy

Author

John Tyler Rascoe, Dec 30 2024

Status

approved