|
|
A127538
|
|
Triangle read by rows: T(n,k) is the number of ordered trees with n edges having k odd-length branches starting at the root (0<=k<=n).
|
|
3
|
|
|
1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 3, 3, 7, 0, 1, 3, 22, 6, 10, 0, 1, 16, 43, 50, 9, 13, 0, 1, 37, 175, 101, 87, 12, 16, 0, 1, 134, 503, 448, 177, 133, 15, 19, 0, 1, 411, 1784, 1305, 862, 271, 188, 18, 22, 0, 1, 1411, 5887, 4848, 2524, 1444, 383, 252, 21, 25, 0, 1, 4747, 20604
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f.=(1+z)/(1+z-z^2*C-tzC), where C =[1-sqrt(1-4z)]/(2z) is the Catalan function.
|
|
EXAMPLE
|
T(2,2)=1 because we have the tree /\.
Triangle starts:
1;
0,1;
1,0,1;
0,4,0,1;
3,3,7,0,1;
3,22,6,10,0,1;
|
|
MAPLE
|
C:=(1-sqrt(1-4*z))/2/z: G:=(1+z)/(1+z-z^2*C-t*z*C): Gser:=simplify(series(G, z=0, 15)): for n from 0 to 12 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 12 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|