OFFSET
1,2
COMMENTS
The expected number of trees in each forest approaches 5/2 as n gets large.
FORMULA
a(n) = Sum_{k=1..n} binomial(n,k)*n^(n-k)*k^2 = ((1 + 1/n)^n n^(1 + n) (-1 + 5 n))/(1 + n)^3.
a(n) = Sum_{k=1..n} A225465(n,k)*k.
EXAMPLE
a(2) = 6 because there are 6 trees in these forests on 2 nodes. The root node is on top and the designated tree is marked by '.
...1'... ...2'... ...1'..2... ...1..2'...
...| ... ...| ... ........... ...........
...2 ... ...1 ... ........... ...........
MATHEMATICA
Table[Sum[Binomial[n - 1, k - 1] n^(n - k) k^2, {k, 1, n}], {n, 1,
20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 08 2013
STATUS
approved