OFFSET
0,2
COMMENTS
Each tree has at least 1 non-root node.
LINKS
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A000108(j+1).
a(n) = A275431(2n,n).
a(n) ~ c * 4^n / n^(3/2), where c = 49.48222899350915021666300344559315... - Vaclav Kotesovec, Sep 27 2017
EXAMPLE
: a(2) = 8: (2 trees in each forest having 4 non-root nodes)
:
: o o . o o . o o . o o . o o . o o . o o . o o .
: | | . | | . | | . ( ) | . ( ) | . | ( ) . /|\ | . ( ) ( ) .
: o o . o o . o o . o o o . o o o . o o o . o o o o . o o o o .
: | . | | . ( ) . | . | . | . . .
: o . o o . o o . o . o . o . . .
: | . . . . . . . .
: o . . . . . . . .
:
MAPLE
C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(C(d+1)
*d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30);
MATHEMATICA
c[n_] := c[n] = Binomial[2n, n]/(n+1);
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[c[d+1] d, {d, Divisors[j]}] a[n-j], {j, 1, n}]/n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 21 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 20 2017
STATUS
approved