%I #9 Jan 03 2024 09:55:49
%S 1,-1,1,1,-1,1,-2,2,-2,1,6,-6,6,-3,1,-30,30,-30,15,-5,1,240,-240,240,
%T -120,40,-8,1,-3120,3120,-3120,1560,-520,104,-13,1,65520,-65520,65520,
%U -32760,10920
%N Number triangle T(n,k)=(-1)^(n-k)*[k<=n]*Product{i=k+1..n,Sum{j=0..i-1,F(j-1)}}.
%C First two subdiagonals are -A000045(n+1) and A001654(n+1). Inverse is A128206.
%e Triangle begins
%e 1,
%e -1, 1,
%e 1, -1, 1,
%e -2, 2, -2, 1,
%e 6, -6, 6, -3, 1,
%e -30, 30, -30, 15, -5, 1,
%e 240, -240, 240, -120, 40, -8, 1,
%e -3120, 3120, -3120, 1560, -520, 104, -13, 1,
%e 65520, -65520, 65520, -32760, 10920, -2184, 273, -21, 1
%K easy,sign,tabl
%O 0,7
%A _Paul Barry_, Feb 19 2007