OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
a(1) = 1; a(n+1) = Sum_{d|n} C(a(n/d) + d-1, d).
EXAMPLE
The tree shown below left counts, because the subtree shown on the left has 3 nodes and so does the one on the right and a similar condition holds for the subtrees. The tree shown on the right is not counted, because the subtree shown on the left has 3 nodes, while the one on the right has 4.
O..........O...O...O
|..........|....\./.
O...O...O..O.....O..
.\...\./....\....|..
.O...O......O...O..
..\./........\./...
...O..........O....
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n<2, n,
add(binomial(a((n-1)/d)+d-1, d), d=divisors(n-1)))
end:
seq(a(n), n=1..50); # Alois P. Heinz, May 16 2013
MATHEMATICA
a[1] = 1; a[n_] := a[n] = DivisorSum[n-1, Binomial[a[(n-1)/#]+#-1, #]&]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Feb 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Jan 17 2007
STATUS
approved