A294951 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(-Sum_{j>=1} sigma_k(j) * x^j).

1, 1, -1, 1, -1, -3, 1, -1, -5, -1, 1, -1, -9, -7, 1, 1, -1, -17, -31, 1, 279, 1, -1, -33, -115, -23, 839, 301, 1, -1, -65, -391, -215, 3399, 4171, 12263, 1, -1, -129, -1267, -1319, 17519, 41311, 54305, 5601, 1, -1, -257, -3991, -6839, 102999, 387031, 473129, 102817, -431281

Offset: 0

Author

Seiichi Manyama, Nov 12 2017

Keywords

• sign
• tabl

Examples

			Square array A(n,k) begins:
     1,   1,    1,     1,      1, ...
    -1,  -1,   -1,    -1,     -1, ...
    -3,  -5,   -9,   -17,    -33, ...
    -1,  -7,  -31,  -115,   -391, ...
     1,   1,  -23,  -215,  -1319, ...
   279, 839, 3399, 17519, 102999, ...
		

Crossrefs

Columns k=0..2 give A294402, A294403, A294404.

Rows n=0..2 give A000012, (-1)*A000012, (-1)*A000051(n+1).

Cf. A294947.

Formula

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