OFFSET
0,5
COMMENTS
FORMULA
T(n, k) = Sum_{i=0..k} T(k, i)*T(n-i-1, k-i) for 0<k<n, else T(0, n)=T(n, n)=1.
EXAMPLE
T(7,3) = T(3,0)*T(6,3) + T(3,1)*T(5,2) + T(3,2)*T(4,1) + T(3,3)*T(3,0)
= 1*70 + 3*16 + 4*4 + 1*1 = 135.
Rows begin:
[1],
[1,1],
[1,2,1],
[1,3,4,1],
[1,4,9,9,1],
[1,5,16,30,24,1],
[1,6,25,70,115,77,1],
[1,7,36,135,344,510,295,1],
[1,8,49,231,805,1908,2602,1329,1],
[1,9,64,364,1616,5325,11904,15133,6934,1],...
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k || k==0, 1, sum(i=0, k, T(k, i)*T(n-i-1, k-i)); ))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Sep 07 2004
STATUS
approved