OFFSET
0,5
FORMULA
T(n,k) = Sum_{j=0..n} (k-1)^(n-j) * binomial(k*n+1,j).
T(n,k) = Sum_{j=0..n} k^(n-j) * binomial((k-1)*n+j,j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 2, 4, 6, 8, 10, ...
0, 3, 16, 39, 72, 115, ...
0, 4, 64, 258, 664, 1360, ...
0, 5, 256, 1719, 6184, 16265, ...
0, 6, 1024, 11496, 57888, 195660, ...
PROG
(PARI) T(n, k) = sum(j=0, n, binomial(k*j, j)*binomial(k*(n-j), n-j));
(PARI) T(n, k) = sum(j=0, n, (k-1)^(n-j)*binomial(k*n+1, j));
(PARI) T(n, k) = sum(j=0, n, k^(n-j)*binomial((k-1)*n+j, j));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 31 2022
STATUS
approved