OFFSET
0,5
FORMULA
T(n, k) = sum_{i=0..n} T(k-1, i)*T(k-1, n-i), with T(n, 0)=T(0, k)=1 for n>=0, k>0.
EXAMPLE
Column 2: {1,4,12,28,56,100,...} equals the self-convolution of row 1: {1,2,4,6,8,10,...}.
Rows begin:
[1,1,1,1,1,1,1,1,1,1,1,1,1,...],
[1,2,4,6,8,10,12,14,16,18,20,22,...],
[1,3,12,33,72,137,236,377,568,817,...],
[1,4,28,138,500,1532,4196,10518,...],
[1,5,56,486,2888,13772,57560,219834,...],
[1,6,100,1498,14792,110856,698816,...],
[1,7,164,4111,67692,812492,7930308,...],
[1,8,252,10210,278396,5364868,...],
[1,9,368,23288,1040856,31939300,...],
[1,10,516,49394,3581120,173226000,...],...
PROG
(PARI) T(n, k)=if(n<0 || k<0, 0, if(n==0 || k==0, 1, sum(i=0, n, T(k-1, i)*T(k-1, n-i))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 30 2004
STATUS
approved