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

1, 0, 1, -1, -1, 1, 2, -3, -3, 1, 3, 20, -3, -6, 1, -44, -29, 80, 5, -10, 1, 145, -399, -354, 205, 30, -15, 1, 714, 3583, -1155, -1764, 385, 84, -21, 1, -12103, -4816, 29014, 1148, -5929, 532, 182, -28, 1, 51128, -202887, -163008, 132726, 23940, -15561, 420, 342, -36, 1, 520191, 2267207, -1085949, -1450530

Offset

1,7

Comments

Row sums are:

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

Links

Table of n, a(n) for n=1..59.

Formula

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)

Example

{1},
{0, 1},
{-1, -1, 1},
{2, -3, -3, 1},
{3, 20, -3, -6, 1},
{-44, -29, 80, 5, -10, 1},
{145, -399, -354,205, 30, -15, 1},
{714, 3583, -1155, -1764, 385, 84, -21, 1},
{-12103, -4816, 29014, 1148, -5929, 532, 182, -28, 1},
{51128, -202887, -163008, 132726, 23940, -15561, 420, 342, -36, 1},
{520191, 2267207, -1085949, -1450530, 397515, 120897, -34083, -390, 585, -45, 1}

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

Crossrefs

Cf. A129065.

Sequence in context: A279004 A172528 A087074 * A114104 A076780 A324733

Adjacent sequences: A136450 A136451 A136452 * A136454 A136455 A136456

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Mar 19 2008

Status

approved