A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j*x^j)^(j^(k*j)) in powers of x.

1, 1, -1, 1, -1, -2, 1, -1, -8, -1, 1, -1, -32, -73, -1, 1, -1, -128, -2155, -919, 5, 1, -1, -512, -58921, -259477, -13977, 1, 1, -1, -2048, -1593811, -67041751, -48496477, -253640, 13, 1, -1, -8192, -43044673, -17178144301, -152513231553, -13001163543, -5290184, 4

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^(k*d+1+j/d)) * 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, ...
   -1, -919, -259477, -67041751, -17178144301, ...

Crossrefs

Columns k=0..2 give A022661, A294606, A294607.

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

Cf. A283675, A294609.

Sequence in context: A072286 A007375 A294808 * A060865 A078689 A230069

Adjacent sequences: A294602 A294603 A294604 * A294606 A294607 A294608

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 04 2017

Status

approved