|
|
A124973
|
|
a(n) = Sum_{k=0..(n-2)/2} a(k)a*(n-1-k), with a(0) = a(1) = 1.
|
|
4
|
|
|
1, 1, 1, 1, 2, 3, 6, 11, 22, 42, 87, 174, 365, 745, 1587, 3303, 7103, 14974, 32477, 69284, 151172, 325077, 713400, 1545719, 3406989, 7423648, 16429555, 35992438, 79912474, 175785514, 391488688, 864591621, 1930333822, 4276537000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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:
|
|
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)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|