%I
%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^(nk) in Product_{m=0..n1} (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(n1) = (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)*(x1) = x^21. Coefficients are 1, 0, and 1.
%e Row 3: (x+(1)^(0)*0!)*(x(1)^(1)*1!)*(x+(1)^(2)*2!) = (x+1)*(x1)*(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
