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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). 0
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 (list; table; graph; refs; listen; history; text; internal format)
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..52.

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

{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},

{-132759147, 290128956, -221191449, 69967716, -3029890, -4304544, 1374390, -201388, 16005, -660, 11}

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: A216217 A253283 A261719 * A257740 A161628 A244119

Adjacent sequences:  A137660 A137661 A137662 * A137664 A137665 A137666

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Apr 27 2008

STATUS

approved

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Last modified January 18 07:18 EST 2019. Contains 319269 sequences. (Running on oeis4.)