OFFSET
1,1
COMMENTS
FORMULA
T(n,k) = 2*binomial(2k-2,k-1)*binomial(2n-2k,n-k)/k.
G.f. = G(t,z) = (1-sqrt(1-4tz))/sqrt(1-4z).
T(n+1,k+1) = 2*(n-k+1)*A078391(n,k), n >= 0, k >= 0. - Philippe Deléham, Dec 13 2006
EXAMPLE
T(3,2)=4 because we have uudd|ud, uudd|du, dduu|ud and dduu|du (first return to the x-axis shown by | ).
Triangle starts:
2;
4, 2;
12, 4, 4;
40, 12, 8, 10;
140, 40, 24, 20, 28;
MAPLE
T:=(n, k)->2*binomial(2*k-2, k-1)*binomial(2*n-2*k, n-k)/k: for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, May 06 2006
STATUS
approved