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A136452 A129065 with v=x instead of v=1: recursive polynomial coefficient triangle. 0

%I #3 Mar 30 2012 17:34:22

%S 1,1,4,0,-1,36,0,-17,4,576,0,-380,148,-15,14400,0,-11804,5908,-1015,

%T 56,518400,0,-496944,290928,-65120,6116,-185,25401600,0,-27460656,

%U 17936112,-4733696,577556,-28385,204,1625702400,0,-1935293184,1371808128,-405733232,57923264,-3462648,-6152,6209

%N A129065 with v=x instead of v=1: recursive polynomial coefficient triangle.

%C Row sums are:

%C {1, 1, 3, 23, 329, 7545, 253195, 11692735, 710944785, 55043460305,

%C 5286546264275}

%F 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)

%e {1},

%e {1},

%e {4, 0, -1},

%e {36, 0, -17,4},

%e {576, 0, -380, 148, -15},

%e {14400, 0, -11804, 5908, -1015,56},

%e {518400, 0, -496944, 290928, -65120, 6116, -185},

%e {25401600, 0, -27460656, 17936112, -4733696, 577556, -28385, 204},

%e {1625702400, 0, -1935293184, 1371808128, -405733232, 57923264, -3462648, -6152,6209},

%e {131681894400, 0, -169764367104, 128290843008, -41266969200, 6529719744, -418217336, -12355080, 3024273, -112400},

%e {13168189440000, 0, -18161573760000, 14454310602240, -4959685865664, 841974673536, -53197348976, -4408319328, 1000552476, -65230280, 1520271}

%t 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]

%Y Cf. A129065.

%K uned,tabl,sign

%O 1,3

%A _Roger L. Bagula_, Mar 19 2008

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Last modified September 13 05:16 EDT 2024. Contains 375859 sequences. (Running on oeis4.)