A275307 Number of labeled spanning blobs on n vertices.

1, 1, 2, 44, 4983, 7565342, 2414249587694, 56130437054842366160898

Offset: 1

Author

Gus Wiseman, Jul 22 2016

Keywords

• nonn
• more

Comments

A clutter is a set of sets comprising a connected antichain in the Boolean algebra B_n. A blob is defined as a clutter that cannot be capped by a tree.

Examples

			The a(3)=2 blobs are: {{1,2,3}}, {{1,2},{1,3},{2,3}}.
		

Links

• Louis J. Billera, On the Composition and Decomposition of Clutters, J. Combinatorial Theory 11, 234-245 (1971).
• Gus Wiseman, Every Clutter is a Tree of Blobs (preprint)

Crossrefs

Cf. A048143 (clutters), A030019 (hypertrees), A052888 (tail trees).

Formula

Every clutter is a tree of blobs, so we have A048143(n) = Sum_p n^(k-1) Prod_i a(|p_i|+1), where the sum is over all set partitions U(p_1,...,p_k) = {1,...,n-1}.