1,4

A rooted trimmed tree is a tree with a forbidden limb of length 2.

A rooted tree with a forbidden limb of length k is a rooted tree where the path from any leaf inward hits a branching node or the root within k steps.

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

F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 78 (1971), 1097-1103.

R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.

K. L. McAvaney, personal communication.

A. J. Schwenk, Almost all trees are cospectral, pp. 275-307 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

a(n) satisfies a=SHIFT_RIGHT(EULER(a-b)) where b(2)=1, b(k)=0 if k != 2.

with (numtheory): a:= proc(n) option remember; local d, j, aa; aa:= n-> a(n)-`if`(n=2, 1, 0); if n<=1 then n else (add (d*aa(d), d=divisors(n-1)) +add (add (d*aa(d), d=divisors(j)) *a(n-j), j=1..n-2))/ (n-1) fi end: seq (a(n), n=1..32); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]

Cf. A002988-A002992, A052318-A052329.

Adjacent sequences: A002952 A002953 A002954 this_sequence A002956 A002957 A002958

Sequence in context: A157904 A002845 A072925 this_sequence A093951 A137255 A076892

nonn,nice,eigen

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

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