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

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, ...
    1,   0,  -6,  -30,  -114,   -390, ...
   -1, -12, -72, -360, -1656,  -7272, ...
   41, 180, 840, 4200, 22440, 126600, ...

Crossrefs

Columns k=0..1 give A028343, A294463.

Rows n=0..3 give A000012, (-1)*A000012, (-1)*A000079, (-1)*A245804.

Cf. A294761.

Sequence in context: A007442 A362483 A054772 * A085384 A067856 A343370

Adjacent sequences: A294613 A294614 A294615 * A294617 A294618 A294619

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 05 2017

Status

approved