OFFSET
0,5
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1080
FORMULA
T(n+k, k) = Sum T(n, j)*k^j {j=0..n}, with T(n, 0)=T(0, n)=1 for n>=0.
EXAMPLE
For row n=3, k=2, T(n+k,k)=T(5,2)=29=(1)+(4)2+(3)2^2+(1)2^3.
For n=4, k=3, T(n+k,k)=T(7,3)=298=(1)+(9)3+(9)3^2+(4)3^3+(1)3^4.
Rows begin with n=0:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 9, 9, 4, 1;
1, 24, 29, 16, 5, 1;
1, 76, 103, 67, 25, 6, 1;
1, 279, 405, 298, 129, 36, 7, 1;
1, 1156, 1757, 1414, 693, 221, 49, 8, 1;
1, 5300, 8355, 7177, 3889, 1396, 349, 64, 9, 1;
1, 26541, 43229, 39016, 22881, 9096, 2539, 519, 81, 10, 1;
1, 143914, 241677, 227074, 141613, 61331, 18901, 4278, 737, 100, 11, 1;
1, 839638, 1451103, 1412233, 924257, 429396, 144349, 35890, 6793, 1009, 121, 12, 1; ...
PROG
(PARI) {T(n, k)=if(n<k||k<0, 0, if(n==k||k==0, 1, sum(j=0, n-k, T(n-k, j)*k^j)))}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Dec 22 2003
STATUS
approved