OFFSET
0,3
COMMENTS
Also for n>0, rooted trees with n nodes and 2-colored internal nodes. Black nodes correspond to nodes with a leaf child; white nodes correspond to those without one.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
FORMULA
Shifts left and halves under WEIGH transform.
a(n) ~ c * d^n / n^(3/2), where d = 4.1516890102085520777311008746639624... and c = 0.3329810927479684511418598248... - Vaclav Kotesovec, Feb 28 2014
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<2, 1, 2*b(n-1, n-1)):
seq(a(n), n=0..30); # Alois P. Heinz, May 20 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 1, 2*b[n-1, n-1]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Jun 07 2005
STATUS
approved