A294616 - OEIS

A294616

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: Product_{j>0} (1-j^k*x^j)^(1/j).

1, 1, -1, 1, -1, -1, 1, -1, -2, 1, 1, -1, -4, 0, -1, 1, -1, -8, -6, -12, 41, 1, -1, -16, -30, -72, 180, -131, 1, -1, -32, -114, -360, 840, -1080, 1499, 1, -1, -64, -390, -1656, 4200, -8640, 15120, -4159, 1, -1, -128, -1266, -7272, 22440, -69120, 161280, -45360

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OFFSET

0,9

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(0,k) = 1 and A(n,k) = -(n-1)! * Sum_{j=1..n} (Sum_{d|j} d^(k*j/d)) * A(n-j,k)/(n-j)! for n > 0.

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, ...

-1, -1, -1, -1, -1, -1, ...

-1, -2, -4, -8, -16, -32, ...