A047991 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,6

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

EXAMPLE

Triangle begins

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;

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 *)

CROSSREFS

A047990 gives sums of absolute values of rows.

Sequence in context: A098509 A019910 A084309 * A296666 A120898 A153910

Adjacent sequences: A047988 A047989 A047990 * A047992 A047993 A047994

KEYWORD

sign,tabl,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved