|
| |
|
|
A101401
|
|
Triangle read by rows: T(n,k) is the number of noncrossing trees with n edges in which the leftmost child of the root has degree k.
|
|
0
| |
|
|
1, 1, 2, 3, 6, 3, 12, 24, 15, 4, 55, 110, 75, 28, 5, 273, 546, 390, 168, 45, 6, 1428, 2856, 2100, 980, 315, 66, 7, 7752, 15504, 11628, 5712, 2040, 528, 91, 8, 43263, 86526, 65835, 33516, 12825, 3762, 819, 120, 9, 246675, 493350, 379500, 198352, 79695, 25410, 6370, 1200, 153, 10
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Row n contains n terms. Column 0 and row sums yield the ternary numbers (A001764).
|
|
|
FORMULA
| T(n, k)=[(k+1)(2k+1)/(3n-k-2)]binomial(3n-k-2, 2n-1). G.f.=zg/(1-tzg^2)^2, where g=1+zg^3 is the g.f. of the ternary numbers (A001764).
|
|
|
EXAMPLE
| T(2,0)=1 and T(2,1)=2 because the noncrossing trees with 2 edges are /\, |_ and _|.
Triangle starts:
1;
1,2;
3,6,3;
12,24,15,4;
55,110,75,28,5;
|
|
|
MAPLE
| T:=proc(n, k) if n=1 and k=1 then 0 elif k<=n then (k+1)*(2*k+1)*binomial(3*n-k-2, 2*n-1)/(3*n-k-2) else 0 fi end: for n from 1 to 10 do seq(T(n, k), k=0..n-1) od; # yields sequence in triangular form
|
|
|
CROSSREFS
| Cf. A001764.
Sequence in context: A129915 A019773 A109536 * A106834 A191658 A021427
Adjacent sequences: A101398 A101399 A101400 * A101402 A101403 A101404
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 15 2005
|
| |
|
|
