0,4

Equivalently, this is the number of "hypertrees" on n labeled nodes, i.e. connected hypergraphs that have no cycles, assuming that each edge contains at least two vertices. - D. E. Knuth, Jan 26 2008. See A134954 for hyperforests.

Also number of labeled connected graphs where every block is a complete graph (cf. A035053).

Let H = (V,E) be the complete hypergraph on N labeled vertices (all edges having cardinality 2 or greater). Let e in E and K = |e|. Then the number of distinct spanning trees of H that contain edge e is g(N,K) = K * E[X_N^{N-K}] / N and the K=1 case gives this sequence. Clearly there is some deep structural connection between spanning trees in hypergraphs and Poisson moments.

Warren D. Smith and David Warme, Paper in preparation, 2002.

T. D. Noe, Table of n, a(n) for n=0..100

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 810

Index entries for sequences related to trees

a(n) = A035051(n)/n, n>0.

a(n) = sum_{i=0...n-1} Stirling2(n-1, i) n^{i-1}, n >= 1.

a(n) = E[X_n^{n-1}] / n, n >= 1, where X_n is a Poisson random variable with mean n.

Cf. A030438, A035051, A035053, A134954, A134956, A134958.

Sequence in context: A089470 A014622 A067146 this_sequence A028853 A118795 A099700

Adjacent sequences: A030016 A030017 A030018 this_sequence A030020 A030021 A030022

nonn,nice

David Warme (warme(AT)s3i.com)

More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net) Dec 15 1999