OFFSET
0,14
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, 2, 3, 4, 5, 6, 7, ...
1, 5, 9, 13, 17, 21, 25, ...
1, 11, 21, 31, 41, 51, 61, ...
1, 31, 81, 151, 241, 351, 481, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\3, (k/6)^j/(j!*(n-3*j)!));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved