1,2

These are series-reduced rooted trees where each leaf is a non-empty subset of the set of n labels.

See A141268 for phylogenetic rooted trees with n unlabeled objects. - Thomas Wieder (thomas.wieder(AT)t-online.de), Jun 20 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Foulds, L. R.; Robinson, R. W. Enumeration of phylogenetic trees without points of degree two. Ars Combin. 17 (1984), A, 169-183. Math. Rev. 85f:05045

T. D. Noe, Table of n, a(n) for n=1..100

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Stirling transform of [ 1, 1, 4, 26, 236, ... ] = A000311 [ Foulds and Robinson ].

G.f.: -LambertW(-1/2*exp(1/2*exp(z)-1))+1/2*exp(z)-1 series(-LambertW(-1/2*exp(1/2*exp(z)-1))+1/2*exp(z)-1,z=0,10). - Thomas Wieder (thomas.wieder(AT)t-online.de), Jun 20 2008

a(3)=8 because we have:

Set(Set(Z[3]),Set(Z[1]),Set(Z[2])),

Set(Z[3],Z[2],Z[1]),

Set(Set(Z[3],Z[1]),Set(Z[2])),

Set(Set(Set(Z[3]),Set(Z[2])),Set(Z[1])),

Set(Set(Set(Z[3]),Set(Z[1])),Set(Z[2])),

Set(Set(Z[3]),Set(Set(Z[1]),Set(Z[2]))),

Set(Set(Z[3]),Set(Z[2],Z[1])),

Set(Set(Z[3],Z[2]),Set(Z[1]))

combstruct command: A005804 := [H, {H=Union(Set(Z, card>=1), Set(H, card>=2))}, labelled]; seq(count(A00584, size=j), j=1..20); - Thomas Wieder (thomas.wieder(AT)t-online.de), Jun 20 2008

Cf. A000311, A005805.

Cf. A141268.

Sequence in context: A153553 A007347 A063074 this_sequence A162067 A086907 A132186

Adjacent sequences: A005801 A005802 A005803 this_sequence A005805 A005806 A005807

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

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