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.
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
Examples
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, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..59, flattened
Crossrefs
Programs
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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
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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 *)
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).