OFFSET
0,4
COMMENTS
A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: 1+x^4/2+x^5/2+x^6/2+B(x)-B(x)^2/2 where B(x) is e.g.f. of A052322.
a(n) ~ (1+LambertW(-3*exp(-3)))^(3/2) * exp(n/3*LambertW(-3*exp(-3))) * n^(n-2). - Vaclav Kotesovec, Mar 29 2014
MATHEMATICA
CoefficientList[Series[1+x^4/2+x^5/2+x^6/2-LambertW[-x*E^(-x^3)]-(LambertW[-x*E^(-x^3)])^2/2, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 29 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Dec 15 1999
STATUS
approved