OFFSET
1,1
COMMENTS
There are no such trees with an odd number of nodes.
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
FORMULA
a(n) = (n/2^n)*Sum_{k=0..n} binomial(n, k)*(n-2*k)^(n-2).
a(n) = 2*n * A007106(n).
a(n) ~ sqrt(1+s^2) * s^(2*n-1) * 2^(2*n) * n^(2*n-1) / exp(2*n), where s = 1.5088795615383199289... is the root of the equation sqrt(1+s^2) = s*log(s+sqrt(1+s^2)). - Vaclav Kotesovec, Jan 23 2014
MAPLE
a:= j-> (n-> (n/2^n)*add(binomial(n, k)*(n-2*k)^(n-2), k=0..n))(2*j):
seq(a(n), n=1..15); # Alois P. Heinz, Sep 27 2020
MATHEMATICA
Flatten[{2, Table[n/2^n*Sum[Binomial[n, k]*(n-2*k)^(n-2), {k, 0, n}], {n, 4, 30, 2}]}] (* Vaclav Kotesovec, Jan 23 2014 *)
PROG
(PARI) a(n) = n/2^n*sum(k=0, n, binomial(n, k)*(n-2*k)^(n-2)) \\ Michel Marcus, Jun 17 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 28 2001
STATUS
approved