OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Emeric Deutsch, Problem 10658: Another Type of Lattice Path, American Math. Monthly, 107, 2000, 368-370.
FORMULA
T(n,k) = (1/n)*binomial(n,k)*binomial(3*n-k,n-1).
G.f.: G = G(t,z) satisfies G=1+z(t+G)G^2.
EXAMPLE
Example T(2,1) = 5 because we have udUdd, uUddd, Uddud, Ududd and UUdddd.
Triangle begins:
1;
1,1;
3,5,2;
12,28,21,5;
...
MAPLE
T:=(n, k)->binomial(n, k)*binomial(3*n-k, n-1)/n: print(1); for n from 1 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
MATHEMATICA
Table[If[n == 0, 1, (1/n)*Binomial[n, k]*Binomial[3 n - k, n - 1]], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Nov 29 2017 *)
PROG
(PARI) for(n=0, 10, for(k=0, n, print1(if(n==0, 1, (1/n)*binomial(n, k) *binomial(3*n-k, n-1)), ", "))) \\ G. C. Greubel, Nov 29 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jun 03 2005
STATUS
approved