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A291556
Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) = (n!)^k * Sum_{i=1..n} 1/i^k.
12
0, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 5, 11, 4, 0, 1, 9, 49, 50, 5, 0, 1, 17, 251, 820, 274, 6, 0, 1, 33, 1393, 16280, 21076, 1764, 7, 0, 1, 65, 8051, 357904, 2048824, 773136, 13068, 8, 0, 1, 129, 47449, 8252000, 224021776, 444273984, 38402064, 109584, 9
OFFSET
0,6
LINKS
FORMULA
A(0, k) = 0, A(1, k) = 1, A(n+1, k) = (n^k+(n+1)^k)*A(n, k) - n^(2*k)*A(n-1, k).
EXAMPLE
Square array begins:
0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, ...
3, 11, 49, 251, 1393, ...
4, 50, 820, 16280, 357904, ...
MAPLE
A:= (n, k)-> n!^k * add(1/i^k, i=1..n):
seq(seq(A(n, d-n), n=0..d), d=0..10); # Alois P. Heinz, Aug 26 2017
MATHEMATICA
A[0, _] = 0; A[1, _] = 1; A[n_, k_] := A[n, k] = ((n-1)^k + n^k) A[n-1, k] - (n-1)^(2k) A[n-2, k];
Table[A[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, May 11 2019 *)
CROSSREFS
Rows n=0-3 give: A000004, A000012, A000051, A074528.
Main diagonal gives A060943.
Sequence in context: A316269 A242379 A103438 * A323073 A167279 A068920
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Aug 26 2017
STATUS
approved