%I #37 Jun 07 2021 14:22:53
%S 1,1,1,1,0,-1,1,2,-1,-2,1,-4,-13,4,12,1,20,-109,-308,108,288,1,-100,
%T -2509,12772,37068,-12672,-34560,1,620,-74509,-1793708,9232908,
%U 26676288,-9158400,-24883200,1,-4420,-3199309,373731652,9049521228,-46507180032,-134457649920,46133452800,125411328000
%N Triangle read by rows: T(n,k) = coefficient of x^(n-k) in Product_{m=0..n-1} (x+(-1)^m*m!), 0 <= k <= n.
%H Jon E. Schoenfield, <a href="/A260612/b260612.txt">Table of n, a(n) for n = 0..1034</a> (first 120 terms from Matthew Campbell)
%F T(n, 1) = A058006(n-1) = (-1)^(n+1)*A153229(n) for n >= 1.
%e Row 0: 1.
%e Row 1: (x+(-1)^(0)*0!) = x+1. Coefficients are 1 and 1.
%e Row 2: (x+(-1)^0*0!)*(x+(-1)^(1)*1!) = (x+1)*(x-1) = x^2-1. Coefficients are 1, 0, and -1.
%e Row 3: (x+(-1)^(0)*0!)*(x-(-1)^(1)*1!)*(x+(-1)^(2)*2!) = (x+1)*(x-1)*(x+2) = x^3 + 2*x^2 - x - 2. Coefficients are 1, 2, -1, and -2.
%Y Cf. A058006, A153229.
%K sign,tabl
%O 0,8
%A _Matthew Campbell_, Aug 08 2015