A293993 Number of unlabeled multiset antichains of weight n.

1, 1, 3, 6, 16, 35, 98, 242, 690

Offset

0,3

Comments

A multiset antichain is a finite set of finite nonempty multisets, none of which is a submultiset of any other. The weight of an antichain is the sum of cardinalities (counting multiplicity) of its elements.

Links

Table of n, a(n) for n=0..8.

Formula

Euler transform of A293994.

Example

Non-isomorphic representatives of the a(4) = 16 antichains are:
((1111)), ((1112)), ((1122)), ((1123)), ((1234)),
((1)(234)), ((2)(111)), ((2)(113)), ((11)(12)), ((11)(22)), ((11)(23)), ((12)(13)), ((12)(34)),
((1)(2)(34)),((2)(3)(11)),
((1)(2)(3)(4)).

Crossrefs

Cf. A007716, A285572, A293606, A293994.

Sequence in context: A327736 A319752 A130095 * A072824 A360229 A369432

Adjacent sequences: A293990 A293991 A293992 * A293994 A293995 A293996

Keyword

nonn,more

Author

Gus Wiseman, Oct 21 2017

Status

approved