OFFSET
0,14
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
E.g.f. of column k: exp(x - k*x^2/2).
T(n,k) = T(n-1,k) - k*(n-1)*T(n-2,k) for n > 1.
T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j / (j! * (n-2*j)!).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, -5, ...
1, -2, -5, -8, -11, -14, -17, ...
1, -2, 1, 10, 25, 46, 73, ...
1, 6, 41, 106, 201, 326, 481, ...
1, 16, 31, -44, -299, -824, -1709, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\2, (-k/2)^j/(j!*(n-2*j)!));
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Apr 13 2023
STATUS
approved