OFFSET
0,20
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
E.g.f. of column k: exp(x - k*x^3/6).
T(n,k) = T(n-1,k) - k * binomial(n-1,2) * T(n-3,k) for n > 2.
T(n,k) = n! * Sum_{j=0..floor(n/3)} (-k/6)^j / (j! * (n-3*j)!).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, -5, ...
1, -3, -7, -11, -15, -19, -23, ...
1, -9, -19, -29, -39, -49, -59, ...
1, -9, 1, 31, 81, 151, 241, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\3, (-k/6)^j/(j!*(n-3*j)!));
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved