A293530 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. 1/Product_{j > 0, j mod k > 0} exp(x^j).

1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, -7, 0, 1, -1, -1, 5, 25, 0, 1, -1, -1, -1, -23, -181, 0, 1, -1, -1, -1, 25, -41, 1201, 0, 1, -1, -1, -1, 1, -101, 1111, -10291, 0, 1, -1, -1, -1, 1, 139, -209, -6259, 97777, 0, 1, -1, -1, -1, 1, 19, -569, 251, -16015

Offset

0,14

Links

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

Formula

E.g.f. of column k: exp((Sum_{j=1..k-1} x^j)/(x^k - 1)).

Example

Square array begins:
   1,    1,   1,    1,   1, ...
   0,   -1,  -1,   -1,  -1, ...
   0,    1,  -1,   -1,  -1, ...
   0,   -7,   5,   -1,  -1, ...
   0,   25, -23,   25,   1, ...
   0, -181, -41, -101, 139, ...

Crossrefs

Columns k=1..3 give A000007, A293532, A293533.

Rows n=0 gives A000012.

Main diagonal gives A293116.

Cf. A293525.

Sequence in context: A136115 A061846 A335947 * A199603 A121570 A169681

Adjacent sequences: A293527 A293528 A293529 * A293531 A293532 A293533

Keyword

sign,tabl

Author

Seiichi Manyama, Oct 11 2017

Status

approved