OFFSET
0,5
COMMENTS
Since T(n,0)=1 for n>=0, then the k-th column of the lower triangular matrix T equals the leftmost column of T^(k+1) for k>=0.
FORMULA
EXAMPLE
T(7,3) = 344 = 1*1 + 9*3 + 9*9 + 4*30 + 1*115
= T(4,0)*T(2,2) +T(4,1)*T(3,2) +T(4,2)*T(4,2) +T(4,3)*T(5,2) +T(4,4)*T(6,2).
Rows begin:
{1},
{1,1},
{1,2,1},
{1,4,3,1},
{1,9,9,4,1},
{1,24,30,16,5,1},
{1,77,115,70,25,6,1},
{1,295,510,344,135,36,7,1},
{1,1329,2602,1908,805,231,49,8,1},
{1,6934,15133,11904,5325,1616,364,64,9,1},...
PROG
(PARI) T(n, k)=if(k>n || n<0 || k<0, 0, if(k==0 || k==n, 1, sum(j=0, n-k, T(n-k, j)*T(j+k-1, k-1)); ); )
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jan 02 2004
STATUS
approved