A137663 Triangular sequence of coefficients from a polynomial recursion: p(x,n)=-2 (-(n - 1) + x)*p(x, n - 1) + (-(n + 1) + (n + 2)* x - x^2)p(x, n - 2).

1, 0, -2, -3, 0, 3, -12, 14, 2, -4, -57, 90, -28, -10, 5, -384, 666, -306, 0, 30, -6, -3441, 6342, -3419, 368, 213, -70, 7, -38220, 74202, -44886, 7834, 1886, -948, 140, -8, -504111, 1023780, -679176, 155604, 15918, -14652, 2880, -252, 9, -7683576, 16226262, -11611074, 3201728, 55680, -243876, 61670, -7224, 420, -10

Offset

1,3

Comments

Row sums are: {1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}

Links

Table of n, a(n) for n=1..55.

Formula

p(x,n)=-2 (-(n - 1) + x)*p[x, n - 1] + (-(n + 1) + (n + 2)* x - x^2)p[x, n - 2]; out_n,m=Coefficients(p(x,n)

Example

Triangle begins:
  {1},
  {0, -2},
  {-3, 0, 3},
  {-12, 14, 2, -4},
  {-57, 90, -28, -10, 5},
  {-384, 666, -306, 0, 30, -6},
  {-3441, 6342, -3419, 368, 213, -70, 7},
  {-38220, 74202, -44886, 7834, 1886, -948, 140, -8},
  {-504111, 1023780, -679176, 155604, 15918, -14652, 2880, -252, 9},
  {-7683576, 16226262, -11611074, 3201728, 55680, -243876, 61670, -7224, 420, -10},
  ...

Mathematica

Clear[p, x] p[x, 0] = 1; p[x, -1] = 0; p[x_, n_] := p[x, n] = -2 (-(n - 1) + x)*p[x, n - 1] + (-(n + 1) + (n + 2)* x - x^2)p[x, n - 2]; g = Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[ CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A253283 A261719 A383583 * A370983 A257740 A161628

Adjacent sequences: A137660 A137661 A137662 * A137664 A137665 A137666

Keyword

tabl,sign

Author

Roger L. Bagula, Apr 27 2008

Status

approved