OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j/d)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 02 2017
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-1, -2, -4, -8, -16, ...
0, -1, -5, -19, -65, ...
0, -1, -7, -37, -175, ...
MATHEMATICA
A[n_, k_] := A[n, k] = If[n == 0, 1, -(1/n)*Sum[Sum[d^(1+k*j/d), {d, Divisors[j]}]*A[n-j, k], {j, 1, n}]];
Table[A[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Sep 04 2022 *)
CROSSREFS
AUTHOR
Seiichi Manyama, Sep 10 2017
STATUS
approved