OFFSET
1,2
LINKS
P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 203-229, 1999.
M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998.
FORMULA
T(n, k) = 2^(k-1)*[(3k-1)/(2n+k-1)]binomial(3n-2, n-k) (1<=k<=n).
G.f.: t*z*g^2/(1-2*t*z*g^3), where g = 1 + z*g^3 is the g.f. of the ternary numbers (A001764).
EXAMPLE
Triangle begins:
1;
2,2;
7,10,4;
30,50,32,8;
143,260,208,88,16;
...
MAPLE
T:=(n, k)->2^(k-1)*(3*k-1)*binomial(3*n-2, n-k)/(2*n+k-1): for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields triangle in triangular form
MATHEMATICA
Flatten[Table[2^(k-1) ((3k-1)/(2n+k-1))Binomial[3n-2, n-k], {n, 10}, {k, n}]] (* Harvey P. Dale, Feb 10 2015 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jan 14 2005
STATUS
approved