A166235 Triangle T(n,m) of the coefficients [x^m] of the polynomial ((x-1)*(x+2)*(x+1))^n, 0<=m<=3n.

1, -2, -1, 2, 1, 4, 4, -7, -8, 2, 4, 1, -8, -12, 18, 35, -6, -33, -10, 9, 6, 1, 16, 32, -40, -120, 1, 160, 76, -80, -74, 0, 20, 8, 1, -32, -80, 80, 360, 70, -601, -430, 405, 540, -10, -268, -110, 30, 35, 10, 1, 64, 192, -144, -992, -420, 1932, 1961, -1512, -2946, -140

Offset

0,2

Comments

The row sums are 1 for row n=0, and 0 for row n>0.

Links

Table of n, a(n) for n=0..60.

Example

1;
-2, -1, 2, 1;
4, 4, -7, -8, 2,4, 1;
-8, -12, 18, 35, -6, -33, -10, 9, 6, 1;
16, 32, -40, -120, 1, 160, 76, -80, -74, 0, 20, 8, 1;
-32, -80,80, 360, 70, -601, -430, 405, 540, -10, -268, -110, 30, 35, 10, 1;
64, 192, -144, -992, -420, 1932, 1961, -1512, -2946, -140, 2031, 1008, -496, -588, -105, 88, 54, 12, 1;
-128, -448, 224, 2576, 1736, -5572, -7686, 4507, 13258, 2163, -11326, -7273, 3906, 5719, 814, -1743, -994, -7, 182, 77, 14, 1;
256, 1024, -256, -6400, -6048, 14784, 26992, -10736, -51967, -16256, 51512, 43456, -21028, -41216, -6808, 18016, 11078, -1664, -4088, -1344, 252, 320, 104, 16, 1;
-512, -2304, 0, 15360, 19008, -36576, -87264, 18000, 183438, 89999, -201438, -222903, 85368, 241884, 56232, -132684, -95004, 21474, 50012, 14526, -9000, -7668, -1368, 756, 510, 135, 18, 1;

Mathematica

Clear[p, x, n, a, b, c, a0]
a = 1; b = -2; c = -1;
p[x_, n_] = ((x - a)*(x - b)*(x - c))^n;
a0 = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[a0]

Crossrefs

Sequence in context: A216327 A099875 A079499 * A143591 A085063 A263078

Adjacent sequences: A166232 A166233 A166234 * A166236 A166237 A166238

Keyword

sign,tabf

Author

Roger L. Bagula and Alexander R. Povolotsky, Oct 09 2009

Status

approved