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Search: id:A136448
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| A136448 |
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A Hermite-like even powered polynomial recursion as a triangle of coefficients: P(x, n) = x^2*P=(x, n - 1) - n^2*P(x, n - 2). |
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1
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| 1, 0, 0, 1, -4, 0, 0, 0, 1, 0, 0, -13, 0, 0, 0, 1, 64, 0, 0, 0, -29, 0, 0, 0, 1, 0, 0, 389, 0, 0, 0, -54, 0, 0, 0, 1, -2304, 0, 0, 0, 1433, 0, 0, 0, -90, 0, 0, 0, 1, 0, 0, -21365, 0, 0, 0, 4079, 0, 0, 0, -139, 0, 0, 0, 1, 147456, 0, 0, 0, -113077, 0, 0, 0, 9839, 0, 0, 0, -203, 0, 0, 0, 1, 0, 0, 1878021, 0, 0, 0, -443476, 0, 0, 0, 21098, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Roe Sums are:
{1, 1, -3, -12, 36, 336, -960, -17424, 44016, 1455360, -2946240};
The double functional integrals show this is nonorthogonal polynomials set:
Table[Table[Integrate[Exp[ -x^2/2]*P[x, n]*P[x, m], {x, -Infinity, Infinity}], {n, 0, 10}], {m, 0, 10}]
for the Hermite weight function on an Infinite domain.
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FORMULA
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P(x,0)=1;P(x,2)=x^2 P(x, n) = x^2*P=(x, n - 1) - n^2*P(x, n - 2)
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EXAMPLE
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{1},
{0, 0, 1},
{-4, 0, 0, 0, 1},
{0, 0, -13, 0, 0, 0, 1},
{64, 0, 0, 0, -29, 0, 0, 0, 1},
{0, 0, 389, 0, 0, 0, -54, 0, 0, 0, 1},
{-2304, 0, 0, 0,1433, 0, 0, 0, -90, 0, 0, 0, 1},
{0, 0, -21365, 0, 0, 0, 4079, 0, 0, 0, -139, 0, 0, 0, 1},
{147456, 0, 0, 0, -113077, 0, 0, 0, 9839, 0, 0, 0, -203, 0, 0, 0, 1},
{0, 0, 1878021, 0, 0, 0, -443476, 0, 0, 0, 21098, 0, 0, 0, -284,0, 0, 0, 1},
{-14745600, 0, 0, 0, 13185721, 0, 0, 0, -1427376, 0,0, 0, 41398, 0, 0, 0, -384, 0, 0, 0, 1}
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MATHEMATICA
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P[x, 0] = 1; P[x, 1] = x^2; P[x_, n_] := P[x, n] = x^2*P[x, n - 1] - n^2*P[x, n - 2]; 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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Adjacent sequences: A136445 A136446 A136447 this_sequence A136449 A136450 A136451
Sequence in context: A108708 A005925 A070206 this_sequence A128975 A028719 A028662
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2008
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