A294808 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*j)*x^j)^j in powers of x.

1, 1, -1, 1, -1, -2, 1, -1, -8, -1, 1, -1, -32, -73, 0, 1, -1, -128, -2155, -927, 4, 1, -1, -512, -58921, -259701, -13969, 4, 1, -1, -2048, -1593811, -67045719, -48496253, -254580, 7, 1, -1, -8192, -43044673, -17178209325, -152513227585, -13001952944, -5288596, 3

Offset

0,6

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^(2+k*j)) * A(n-j,k) for n > 0.

Example

Square array begins:
    1,      1,         1,             1,                1, ...
   -1,     -1,        -1,            -1,               -1, ...
   -2,     -8,       -32,          -128,             -512, ...
   -1,    -73,     -2155,        -58921,         -1593811, ...
    0,   -927,   -259701,     -67045719,     -17178209325, ...
    4, -13969, -48496253, -152513227585, -476819162106101, ...

Crossrefs

Columns k=0..2 give A073592, A294809, A294953.

Rows n=0..2 give A000012, (-1)*A000012, (-1)*A004171.

Cf. A294653, A294950.

Sequence in context: A354986 A072286 A007375 * A294605 A060865 A078689

Adjacent sequences: A294805 A294806 A294807 * A294809 A294810 A294811

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 09 2017

Status

approved