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
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
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