1,4

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 188 (3.1.94)

F. Harary and E. M. Palmer, Graphical Enumeration. New York: Academic Press, 1973. (gives g.f. for unlabeled series-reduced trees.)

P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,'' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.

A. Meir and J. W. Moon, On nodes of degree two in random trees, Mathematika 15 1968 188-192.

R. C. Read, personal communication.

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

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

Eric Weisstein's World of Mathematics, Eric Weisstein, Link to a section of The World of Mathematics.

Index entries for sequences related to trees

a(n) = Sum_{k=0..n-2} ((-1)^k*(n-k)^(n-k-2)*binomial(n, k)*(n-2)!/(n-k-2)!, n>=2.

E.g.f.: (1+x)*B(x)*(1-B(x)/2), where B(x) is e.g.f. for A060356. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 17 2004

a(6) = 96 because there are two unlabeled series-reduced trees on six vertices, the star and the tree with two vertices of degree three and four leaves; the first of these can be labeled in 6 ways and the second in 90, for a total of 96. - Isabel C. Lugo (izzycat(AT)gmail.com), Aug 19 2004

a(n) = A060313(n)/n. Cf. A000014 (labeled analogue).

Sequence in context: A109348 A078985 A041173 this_sequence A052320 A079197 A113942

Adjacent sequences: A005509 A005510 A005511 this_sequence A005513 A005514 A005515

nonn,nice

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

Formula by Christian G. Bower (bowerc(AT)usa.net), Jan 16 2004