|
|
A065329
|
|
Square array read by antidiagonals giving number of binary trees of height n with k points on the n-th level (n,k>0).
|
|
3
|
|
|
1, 0, 2, 0, 1, 8, 0, 0, 8, 80, 0, 0, 4, 144, 4160, 0, 0, 1, 168, 13888, 5632640, 0, 0, 0, 138, 31776, 36109952, 5163215782400, 0, 0, 0, 80, 54792, 158572864, 64827181969920, 2169236189050838782284800, 0, 0, 0, 32, 74624, 531441232, 552146121580800
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = Sum_{2j >= k} (C(2j,k)*T(n-1,j)) starting with T(1,1) = 1 and T(1,k) = 0 if k>1.
|
|
EXAMPLE
|
Square array starts:
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
2, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
8, 8, 4, 1, 0, 0, 0, 0, 0, 0, ...
80, 144, 168, 138, 80, 32, 8, 1, 0, 0, ...
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|