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A294583
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)^(j^k).
3
1, 1, -1, 1, -1, -1, 1, -1, -4, 0, 1, -1, -16, -5, 0, 1, -1, -64, -65, -3, 1, 1, -1, -256, -665, -79, 23, 0, 1, -1, -1024, -6305, -1575, 831, 44, 1, 1, -1, -4096, -58025, -28255, 33335, 4789, 104, 0, 1, -1, -16384, -527345, -481623, 1323807, 411664, 15099, 70, 0
OFFSET
0,9
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+k*j/d)) * 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, -5, -65, -665, -6305, ...
0, -3, -79, -1575, -28255, ...
CROSSREFS
Columns k=0..2 give A010815, A266964, A294584.
Rows n=0..1 give A000012, (-1)*A000012.
Cf. A294585.
Sequence in context: A324563 A186372 A200893 * A283675 A294653 A126222
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 03 2017
STATUS
approved