OFFSET
0,3
LINKS
FORMULA
a(n) = 1 if n=0 and a(n) = n! * Sum_{k=1..n} Sum_{i=1..floor(n/k)} i^(n-k*i)/ ((n-k*i)!*i!*k!^i) else.
EXAMPLE
a(2) = 4, because 4 forests with 2 labels exist: {1}{2}, {1}<-2, {2}<-1, {1,2}.
MAPLE
a:= n-> if n=0 then 1 else n! * add(add(i^(n-k*i)/
((n-k*i)!*i!*k!^i), i=1..floor(n/k)), k=1..n) fi:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 12 2008
STATUS
approved