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Search: id:A137663
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| A137663 |
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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). |
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+0
1
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are: {1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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FORMULA
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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)
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A079777 A047773 A035549 this_sequence A161628 A122059 A164917
Adjacent sequences: A137660 A137661 A137662 this_sequence A137664 A137665 A137666
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KEYWORD
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tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
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