VOOZH about

URL: https://oeis.org/A292166

⇱ A292166 - OEIS

login
A292166
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j^k*x^j).
7
1, 1, -1, 1, -1, -1, 1, -1, -2, 0, 1, -1, -4, -1, 0, 1, -1, -8, -5, -1, 1, 1, -1, -16, -19, -7, 5, 0, 1, -1, -32, -65, -37, 27, 1, 1, 1, -1, -64, -211, -175, 155, 17, 13, 0, 1, -1, -128, -665, -781, 927, 205, 167, 4, 0, 1, -1, -256, -2059, -3367, 5675, 2129, 2089, 110, 0, 0
OFFSET
0,9
LINKS
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
Columns k=0..2 give A010815, A022661, A292164.
Rows n=0..2 give A000012, (-1)*A000012, (-1)*A000079.
Main diagonal gives A292167.
Sequence in context: A362379 A144740 A283272 * A282192 A049501 A102564
KEYWORD
sign,look,tabl
AUTHOR
Seiichi Manyama, Sep 10 2017
STATUS
approved