A136452 A129065 with v=x instead of v=1: recursive polynomial coefficient triangle.
1, 1, 4, 0, -1, 36, 0, -17, 4, 576, 0, -380, 148, -15, 14400, 0, -11804, 5908, -1015, 56, 518400, 0, -496944, 290928, -65120, 6116, -185, 25401600, 0, -27460656, 17936112, -4733696, 577556, -28385, 204, 1625702400, 0, -1935293184, 1371808128, -405733232, 57923264, -3462648, -6152, 6209
Offset: 1
Examples
{1},
{1},
{4, 0, -1},
{36, 0, -17,4},
{576, 0, -380, 148, -15},
{14400, 0, -11804, 5908, -1015,56},
{518400, 0, -496944, 290928, -65120, 6116, -185},
{25401600, 0, -27460656, 17936112, -4733696, 577556, -28385, 204},
{1625702400, 0, -1935293184, 1371808128, -405733232, 57923264, -3462648, -6152,6209},
{131681894400, 0, -169764367104, 128290843008, -41266969200, 6529719744, -418217336, -12355080, 3024273, -112400},
{13168189440000, 0, -18161573760000, 14454310602240, -4959685865664, 841974673536, -53197348976, -4408319328, 1000552476, -65230280, 1520271}
Crossrefs
Cf. A129065.
Programs
-
Mathematica
Clear[p, v, x, n] p[ -1, x] = 0 ; p[0, x] = 1; p[n_, x_] := p[n, x] = (x + 2*(n - 1)^2 - 2*(v - 1)*(n - 1) - v + 1)*p[n - 1, x] - (n - 1)^2*(n - 1 - v)^2*p[n - 2, x]; v = x; a = Join[{{1}}, Table[CoefficientList[p[n, x], x], {n, 1, 10}]]; Flatten[a]
Formula
v=x; p(n, x) = (x + 2*(n - 1)^2 - 2*(v - 1)*(n - 1) - v + 1)*p(n - 1, x) - (n - 1)^2*(n - 1 - v)^2*p(n - 2, x)
Comments