OFFSET
0,3
LINKS
Seiichi Manyama, Antidiagonals n = 0..59, flattened
FORMULA
T(0,k) = 1 and T(n,k) = n^k * T(n-1,k) + 1 for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, ...
3, 5, 9, 17, 33, 65, ...
4, 16, 82, 460, 2674, 15796, ...
5, 65, 1313, 29441, 684545, 16175105, ...
6, 326, 32826, 3680126, 427840626, 50547203126, ...
MATHEMATICA
T[n_, k_] := Sum[(n!/j!)^k, {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, May 03 2021 *)
PROG
(PARI) T(n, k) = sum(j=0, n, (n!/j!)^k);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 02 2021
STATUS
approved