A128207 Number triangle T(n,k)=(-1)^(n-k)*[k<=n]*Product{i=k+1..n,Sum{j=0..i-1,F(j-1)}}.

1, -1, 1, 1, -1, 1, -2, 2, -2, 1, 6, -6, 6, -3, 1, -30, 30, -30, 15, -5, 1, 240, -240, 240, -120, 40, -8, 1, -3120, 3120, -3120, 1560, -520, 104, -13, 1, 65520, -65520, 65520, -32760, 10920

Offset: 0

Author

Paul Barry, Feb 19 2007

Keywords

• easy
• sign
• tabl

Comments

First two subdiagonals are -A000045(n+1) and A001654(n+1). Inverse is A128206.

Examples

			Triangle begins
1,
-1, 1,
1, -1, 1,
-2, 2, -2, 1,
6, -6, 6, -3, 1,
-30, 30, -30, 15, -5, 1,
240, -240, 240, -120, 40, -8, 1,
-3120, 3120, -3120, 1560, -520, 104, -13, 1,
65520, -65520, 65520, -32760, 10920, -2184, 273, -21, 1