OFFSET
0,8
FORMULA
E.g.f. of column k: 1/(1 - k*x*exp(x)).
T(0,k) = 1 and T(n,k) = k * n * Sum_{j=0..n-1} binomial(n-1,j) * T(j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 4, 12, 24, 40, 60, ...
0, 21, 102, 279, 588, 1065, ...
0, 148, 1160, 4332, 11536, 25220, ...
0, 1305, 16490, 84075, 282900, 746525, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n, k^(n-j)*(n-j)^j/j!);
(PARI) T(n, k) = if(n==0, 1, k*n*sum(j=0, n-1, binomial(n-1, j)*T(j, k)));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Feb 18 2022
STATUS
approved