A294254 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1-x^j) - 1).

1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, -1, 0, 1, -1, -1, 11, 1, 0, 1, -1, -1, 5, -23, -1, 0, 1, -1, -1, 5, 25, -101, 1, 0, 1, -1, -1, 5, 1, -41, 991, -1, 0, 1, -1, -1, 5, 1, 199, -1769, -1849, 1, 0, 1, -1, -1, 5, 1, 79, -1409, 7181, -24751, -1, 0, 1, -1, -1, 5

Offset: 0

Author

Seiichi Manyama, Oct 26 2017

Keywords

• sign
• tabl

Examples

			Square array A(n,k) begins:
   1,  1,    1,   1,   1, ...
   0, -1,   -1,  -1,  -1, ...
   0,  1,   -1,  -1,  -1, ...
   0, -1,   11,   5,   5, ...
   0,  1,  -23,  25,   1, ...
   0, -1, -101, -41, 199, ...
		

Links

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

Crossrefs

Columns k=0..5 give A000007, A033999, A294255, A294256, A294257, A294258.

Rows n=0 gives A000012.

Main diagonal gives A294260.

Cf. A294250.

Formula

B(j,k) is the coefficient of Product_{i=1..k} (1-x^i).

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.