A293139 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} Sum_{j=0..k} (-1)^j*x^(j*i)/j!.

1, 1, 0, 1, -1, 0, 1, -1, -2, 0, 1, -1, -1, 0, 0, 1, -1, -1, 0, 0, 0, 1, -1, -1, -1, 0, 120, 0, 1, -1, -1, -1, 0, 0, 0, 0, 1, -1, -1, -1, 1, 20, 180, 5040, 0, 1, -1, -1, -1, 1, 20, 180, 0, 0, 0, 1, -1, -1, -1, 1, 19, 150, 1260, 10080, 0, 0, 1, -1, -1, -1, 1, 19

Offset

0,9

Links

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

Example

Square array begins:
   1,   1,  1,  1,  1, ...
   0,  -1, -1, -1, -1, ...
   0,  -2, -1, -1, -1, ...
   0,   0,  0, -1, -1, ...
   0,   0,  0,  0,  1, ...
   0, 120,  0, 20, 20, ...

Crossrefs

Columns k=0..2 give A000007, A293140, A293141.

Rows n=0 gives A000012.

Main diagonal gives A293116.

Cf. A293135.

Sequence in context: A357375 A133008 A102550 * A351319 A213725 A213726

Adjacent sequences: A293136 A293137 A293138 * A293140 A293141 A293142

Keyword

sign,tabl,look

Author

Seiichi Manyama, Oct 01 2017

Status

approved