A047991 Triangle formed from expansion of (x-1)(x+2)(x-3)...(x+-n).

1, 1, -1, 1, 1, -2, 1, -2, -5, 6, 1, 2, -13, -14, 24, 1, -3, -23, 51, 94, -120, 1, 3, -41, -87, 400, 444, -720, 1, -4, -62, 200, 1009, -2356, -3828, 5040, 1, 4, -94, -296, 2609, 5716, -22676, -25584, 40320, 1, -5, -130, 550, 5273, -17765, -74120, 178500, 270576, -362880

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• tabl
• easy
• nice

Examples

			Triangle begins
  1;
  1, -1;
  1,  1,  -2;
  1, -2,  -5,    6;
  1,  2, -13,  -14,   24;
  1, -3, -23,   51,   94,  -120;
  1,  3, -41,  -87,  400,   444,   -720;
  1, -4, -62,  200, 1009, -2356,  -3828,   5040;
  1,  4, -94, -296, 2609,  5716, -22676, -25584, 40320;
		

References

• Studied by M. Bhargava (bhargava(AT)math.Princeton.EDU) and H. S. Wilf.

Links

• T. D. Noe, Rows n=0..100 of triangle, flattened

Crossrefs

A047990 gives sums of absolute values of rows.

Programs

Mathematica

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 *)