OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..52, flattened
FORMULA
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j)) * A(n-j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-1, -4, -16, -64, -256, ...
0, -23, -713, -19619, -531185, ...
0, -229, -64807, -16757533, -4294435855, ...
MATHEMATICA
rows = 10;
col[k_] := col[k] = CoefficientList[Product[(1 - j^(k*j)*x^j), {j, 1, rows + 3}] + O[x]^(rows + 3), x];
A[n_, k_] := col[k][[n + 1]];
(* or: *)
A[0, _] = 1; A[n_, k_] := A[n, k] = -(1/n)*Sum[DivisorSum[j, #^(1 + k*j) &]*A[n - j, k], {j, 1, n}];
Table[A[n - k, k], {n, 0, rows - 1}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 10 2017 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 06 2017
STATUS
approved