login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #5 Mar 05 2015 13:34:46

%S 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,

%T -120,1,160,76,-80,-74,0,20,8,1,-32,-80,80,360,70,-601,-430,405,540,

%U -10,-268,-110,30,35,10,1,64,192,-144,-992,-420,1932,1961,-1512,-2946,-140

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

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

%e 1;

%e -2, -1, 2, 1;

%e 4, 4, -7, -8, 2,4, 1;

%e -8, -12, 18, 35, -6, -33, -10, 9, 6, 1;

%e 16, 32, -40, -120, 1, 160, 76, -80, -74, 0, 20, 8, 1;

%e -32, -80,80, 360, 70, -601, -430, 405, 540, -10, -268, -110, 30, 35, 10, 1;

%e 64, 192, -144, -992, -420, 1932, 1961, -1512, -2946, -140, 2031, 1008, -496, -588, -105, 88, 54, 12, 1;

%e -128, -448, 224, 2576, 1736, -5572, -7686, 4507, 13258, 2163, -11326, -7273, 3906, 5719, 814, -1743, -994, -7, 182, 77, 14, 1;

%e 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;

%e -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;

%t Clear[p, x, n, a, b, c, a0]

%t a = 1; b = -2; c = -1;

%t p[x_, n_] = ((x - a)*(x - b)*(x - c))^n;

%t a0 = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];

%t Flatten[a0]

%K sign,tabf

%O 0,2

%A _Roger L. Bagula_ and _Alexander R. Povolotsky_, Oct 09 2009