1,2

Series-reduced planted binary trees where each leaf is a non-empty subset of the set of n labels.

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 binary phylogenetic trees. Combinatorial mathematics, VIII (Geelong, 1980), pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. Math. Rev. 83a:05071.

N. J. A. Sloane, Table of n, a(n) for n = 1..101

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 160

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Stirling transform of A001147(n-1).

egf: E^x/(3 - 2E^x)^(1/2) . This sequence is the Stirling transform of the sequence ( (2n-1)!! + n(2n-3)!! )_(n>=0) = (1, 2, 5, 24, 165, 1470, 16065, 207900,...) with egf (1+x)/(1-2x)^(1/2). (Both remarks assume offset 0.) - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008

stirtr:= proc(p) proc (n) add (p(k) *combinat[stirling2] (n, k), k=0..n) end end: f:= n-> `if`(n=0, 1, (2*n-2)!/ (n-1)!/ 2^(n-1)): a:= stirtr(f): seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 15 2008]

Sequence in context: A106871 A107376 A087804 this_sequence A101390 A113144 A006846

Adjacent sequences: A006674 A006675 A006676 this_sequence A006678 A006679 A006680

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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