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A343863
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = (n!)^k * Sum_{j=1..n} (1/j!)^k.
2
1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 9, 16, 5, 1, 2, 17, 82, 65, 6, 1, 2, 33, 460, 1313, 326, 7, 1, 2, 65, 2674, 29441, 32826, 1957, 8, 1, 2, 129, 15796, 684545, 3680126, 1181737, 13700, 9, 1, 2, 257, 94042, 16175105, 427840626, 794907217, 57905114, 109601, 10
OFFSET
0,3
LINKS
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
Columns 0..3 give A000027(n+1), A000522, A006040, A217284.
Main diagonal gives A336247.
Cf. A291556.
Sequence in context: A209564 A029653 A067763 * A263683 A087730 A263736
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 02 2021
STATUS
approved