OFFSET
0,5
FORMULA
E.g.f. of column k: exp( x/(1-x)^k ) / (1-x)^k.
T(n,k) = Sum_{j=0..n} (n+(k-1)*(j+1))!/(k*j+k-1)! * binomial(n,j) for k > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 7, 15, 25, 37, 51, ...
1, 34, 103, 214, 373, 586, ...
1, 209, 885, 2293, 4721, 8481, ...
1, 1546 ,9051, 29176, 70981, 146046, ...
PROG
(PARI) T(n, k) = n! * sum(j=0, n, binomial(n+(k-1)*(j+1), n-j)/j!);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 18 2023
STATUS
approved