OFFSET
0,5
COMMENTS
Number of unordered rooted trees with all outdegrees <= 2 and, if a node has two subtrees, they have a different number of nodes (equivalently, ordered rooted trees where the left subtree has more nodes than the right subtree).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
Lim_{n->infinity} a(n)^(1/n) = 2.327833478... - Vaclav Kotesovec, Nov 20 2019
MAPLE
a:= proc(n) option remember;
if n<2 then 1
else add(a(j)*a(n-j-1), j=0..floor((n-2)/2))
fi
end:
seq(a(n), n=0..40); # G. C. Greubel, Nov 19 2019
MATHEMATICA
a[n_]:= a[n]= If[n<2, 1, Sum[a[j]*a[n-j-1], {j, 0, (n-2)/2}]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Nov 19 2019 *)
PROG
(PARI) a(n) = if(n<2, 1, sum(j=0, (n-2)\2, a(j)*a(n-j-1))); \\ G. C. Greubel, Nov 19 2019
(Sage)
@CachedFunction
def a(n):
if (n<2): return 1
else: return sum(a(j)*a(n-j-1) for j in (0..floor((n-2)/2)))
[a(n) for n in (0..40)] # G. C. Greubel, Nov 19 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Franklin T. Adams-Watters, Nov 14 2006
STATUS
approved