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%I #17 Sep 25 2021 06:51:21
%S 1,1,-1,1,1,-2,1,-2,-5,6,1,2,-13,-14,24,1,-3,-23,51,94,-120,1,3,-41,
%T -87,400,444,-720,1,-4,-62,200,1009,-2356,-3828,5040,1,4,-94,-296,
%U 2609,5716,-22676,-25584,40320,1,-5,-130,550,5273,-17765,-74120,178500,270576,-362880
%N Triangle formed from expansion of (x-1)(x+2)(x-3)...(x+-n).
%D Studied by M. Bhargava (bhargava(AT)math.Princeton.EDU) and H. S. Wilf.
%H T. D. Noe, <a href="/A047991/b047991.txt">Rows n=0..100 of triangle, flattened</a>
%e Triangle begins
%e 1;
%e 1, -1;
%e 1, 1, -2;
%e 1, -2, -5, 6;
%e 1, 2, -13, -14, 24;
%e 1, -3, -23, 51, 94, -120;
%e 1, 3, -41, -87, 400, 444, -720;
%e 1, -4, -62, 200, 1009, -2356, -3828, 5040;
%e 1, 4, -94, -296, 2609, 5716, -22676, -25584, 40320;
%t With[{nn=10},Flatten[Table[Reverse[CoefficientList[Series[Times@@ Table[x+n (-1)^n,{n,i}],{x,0,nn}],x]],{i,0,nn}]]] (* _Harvey P. Dale_, Aug 28 2012 *)
%Y A047990 gives sums of absolute values of rows.
%K sign,tabl,easy,nice
%O 0,6
%A _N. J. A. Sloane_
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