A293299 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} 1/(Sum_{j=0..k} x^(j*i)/j!).

1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, -1, -6, 0, 1, -1, -1, 0, 24, 0, 1, -1, -1, -1, -6, -120, 0, 1, -1, -1, -1, 2, 30, 720, 0, 1, -1, -1, -1, 1, 10, 270, -5040, 0, 1, -1, -1, -1, 1, 20, 170, 0, 80640, 0, 1, -1, -1, -1, 1, 19, 140, 1050, 2520, -725760, 0, 1, -1

Offset

0,14

Links

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

Example

Square array begins:
   1,    1,  1,  1,  1, ...
   0,   -1, -1, -1, -1, ...
   0,    0, -1, -1, -1, ...
   0,   -6,  0, -1, -1, ...
   0,   24, -6,  2,  1, ...
   0, -120, 30, 10, 20, ...

Crossrefs

Columns k=0..1 give A000007, A293300.

Rows n=0 gives A000012.

Main diagonal gives A293116.

Cf. A293135, A293301.

Sequence in context: A076413 A154305 A158781 * A293486 A195398 A063085

Adjacent sequences: A293296 A293297 A293298 * A293300 A293301 A293302

Keyword

sign,tabl

Author

Seiichi Manyama, Oct 05 2017

Status

approved