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A275307 Number of labeled spanning blobs on n vertices. 38


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

%N Number of labeled spanning blobs on n vertices.

%C 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.

%H Louis J. Billera, <a href="http://dx.doi.org/10.1016/0095-8956(71)90033-5">On the Composition and Decomposition of Clutters</a>, J. Combinatorial Theory 11, 234-245 (1971).

%H Gus Wiseman, <a href="https://docs.google.com/document/d/1Okx0eXfCCAVM0lbZ2NoFxIJdprOMdBaxZf26Iu-SXSs/pub">Every Clutter is a Tree of Blobs (preprint)</a>

%F 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}.

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

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

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Jul 22 2016

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Last modified June 13 05:41 EDT 2021. Contains 344981 sequences. (Running on oeis4.)