OFFSET
0,6
FORMULA
EXAMPLE
Rows begin:
[1],
[1,1,0],
[1,2,2,5,0],
[1,3,5,14,14,42,0],
[1,4,9,28,42,132,132,429,0],
[1,5,14,48,90,297,429,1430,1430,4862,0],
[1,6,20,75,165,572,1001,3432,4862,16796,16796,58786,0],...
and is derived from the square array of Catalan convolutions (A033184)
by shifting each column k down by [k/2] rows.
PROG
(PARI) {T(n, k) = if(n==k&k==0, 1, binomial(n+2*k-(k\2), k)*(n-(k\2))/(n+2*k-(k\2)))}
for(n=0, 10, for(k=0, 2*n, print1(T(n, k), ", ")); print(""))
(PARI) {T(n, k) = polcoeff(((1-sqrt(1-4*z +z*O(z^(2*n))))/(2*z))^(n-k\2), k, z)}
for(n=0, 10, for(k=0, 2*n, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul D. Hanna, Nov 09 2004
STATUS
approved