OFFSET
0,7
COMMENTS
LINKS
Emeric Deutsch, Problem 10658: Another Type of Lattice Path, American Math. Monthly, 107, 2000, 368-370.
FORMULA
T(n,k) = binomial(n,2n-k)*binomial(n+k, n-1)/n.
G.f.: G = G(t, z) satisfies G=1+tzG^2*(1+tG).
EXAMPLE
Example T(2,3) = 5 because we have udUdd, uUddd, Uddud, Ududd and Uuddd.
Triangle begins:
1;
0,1,1;
0,0,2,5,3;
0,0,0,5,21,28,12;
...
MAPLE
a:=proc(n, k) if n=0 and k=0 then 1 elif n=0 then 0 elif k=0 then 0 else binomial(n, 2*n-k)*binomial(n+k, n-1)/n fi end: for n from 0 to 8 do seq(a(n, k), k=0..2*n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jun 03 2005
STATUS
approved