A334561 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals downwards, where column k is the expansion of e.g.f. exp(-Sum_{j=1..k} x^j).

1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 5, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 25, -41, 1, 1, -1, -1, -1, 1, 19, 31, -1, 1, -1, -1, -1, 1, 139, -209, 461, 1, 1, -1, -1, -1, 1, 19, 151, -2269, -895, -1, 1, -1, -1, -1, 1, 19, 871, -1429, 2801, -6481, 1, 1, -1, -1, -1, 1, 19, 151, 1091, -19039, 68615, 22591, -1

Offset: 0

Author

Seiichi Manyama, May 06 2020

Keywords

• sign
• tabl

Examples

			Square array begins:
   1,   1,    1,   1,   1,   1,   1, ...
  -1,  -1,   -1,  -1,  -1,  -1,  -1, ...
   1,  -1,   -1,  -1,  -1,  -1,  -1, ...
  -1,   5,   -1,  -1,  -1,  -1,  -1, ...
   1,   1,   25,   1,   1,   1,   1, ...
  -1, -41,   19, 139,  19,  19,  19, ...
   1,  31, -209, 151, 871, 151, 151, ...
		

Links

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

Crossrefs

Columns k=1..5 give A033999, A000321, A334562, A334564, A334565.

Main diagonal gives A293116.

Cf. A293669, A334568.

Formula

A(0,k) = 1 and A(n,k) = - (n-1)! * Sum_{j=1..min(k,n)} j*A(n-j,k)/(n-j)!.