%I #10 Mar 31 2024 17:26:41
%S 1,-1,1,1,-1,1,-3,3,-3,1,15,-15,15,-5,1,-165,165,-165,55,-11,1,3465,
%T -3465,3465,-1155,231,-21,1,-148995,148995,-148995,49665,-9933,903,
%U -43,1,12664575,-12664575,12664575
%N Number triangle T(n,k) = (-1)^(n-k)*[k<=n]*Product_{i=k+1..n} Sum_{j=0..i-1} A078008(j-1).
%C Inverse is A128208. Subdiagonals include -A001045(n+1) and A084175(n+1).
%e Triangle begins:
%e 1;
%e -1, 1;
%e 1, -1, 1;
%e -3, 3, -3, 1;
%e 15, -15, 15, -5, 1;
%e -165, 165, -165, 55, -11, 1;
%e 3465, -3465, 3465, -1155, 231, -21, 1;
%e -148995, 148995, -148995, 49665, -9933, 903, -43, 1;
%e ...
%K easy,sign,tabl
%O 0,7
%A _Paul Barry_, Feb 19 2007