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 A136453 A129065 with v=n instead of v=1: recursive polynomial coefficient triangle. 0

%I

%S 1,0,1,-1,-1,1,2,-3,-3,1,3,20,-3,-6,1,-44,-29,80,5,-10,1,145,-399,

%T -354,205,30,-15,1,714,3583,-1155,-1764,385,84,-21,1,-12103,-4816,

%U 29014,1148,-5929,532,182,-28,1,51128,-202887,-163008,132726,23940,-15561,420,342,-36,1,520191,2267207,-1085949,-1450530

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

%C Row sums are:

%C {1, 1, -1, -3, 15, 3, -387, 1827, 8001, -172935, 735399}

%F v=n; 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 {0, 1},

%e {-1, -1, 1},

%e {2, -3, -3, 1},

%e {3, 20, -3, -6, 1},

%e {-44, -29, 80, 5, -10, 1},

%e {145, -399, -354,205, 30, -15, 1},

%e {714, 3583, -1155, -1764, 385, 84, -21, 1},

%e {-12103, -4816, 29014, 1148, -5929, 532, 182, -28, 1},

%e {51128, -202887, -163008, 132726, 23940, -15561, 420, 342, -36, 1},

%e {520191, 2267207, -1085949, -1450530, 397515, 120897, -34083, -390, 585, -45, 1}

%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 = n; a = Join[{{1}}, Table[CoefficientList[p[n, x], x], {n, 1, 10}]]; Flatten[a]

%Y Cf. A129065.

%K uned,tabl,sign

%O 1,7

%A _Roger L. Bagula_, Mar 19 2008

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)