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A260612 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. 1

%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^(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

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)