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Search: id:A136532
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| A136532 |
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Coefficients of Laguerre recursive polynomials with an (n+2)!/2 multiplication factor and alpha=a0 =-1 from Hochstadt: P(x, n) = (2*n + a0 + 1 - x)*P(x, n - 1)/(n + 1) - n*P(x, n - 2)/(n + 1);. |
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+0
1
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| 1, 0, -3, -8, -16, 4, -60, -65, 50, -5, -384, -168, 462, -108, 6, -2380, 763, 3836, -1624, 196, -7, -14208, 21248, 29560, -21472, 4256, -320, 8, -73836, 302571, 199998, -269127, 78840, -9387, 486, -9, -176000, 3761240, 854530, -3288940, 1360150, -228880, 18430, -700, 10, 3824964, 44711623
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Table[Apply[Plus, CoefficientList[(n + 2)!P[x, n]/2, x]], {n, 0, 10}];
Row sums:
{1, -3, -20, -80, -192, 784, 19072, 229536, 2299840, 20282944, 144429312}
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REFERENCES
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page 8 and page 42 - 43; Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986
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FORMULA
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a0=-1; p(x,0)=1;p(x,1)=1+a0-x; P(x, n) = (2*n + a0 + 1 - x)*P(x, n - 1)/(n + 1) - n*P(x, n - 2)/(n + 1);
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EXAMPLE
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{1},
{0, -3},
{-8, -16, 4},
{-60, -65,50, -5},
{-384, -168, 462, -108, 6},
{-2380, 763, 3836, -1624, 196, -7},
{-14208, 21248, 29560, -21472, 4256, -320, 8},
{-73836, 302571, 199998, -269127, 78840, -9387, 486, -9},
{-176000, 3761240, 854530, -3288940, 1360150, -228880, 18430, -700, 10},
{3824964, 44711623, -7017472, -39417422, 22743644, -5098676, 568568, -33242,968, -11},
{104573760, 520004832, -304428396, -457688256,376007784, -108589488, 15755712, -1261536, 56184, -1296, 12}
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MATHEMATICA
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a0 = -1; P[x, 0] = 1; P[x, 1] = 1 + a0 - x; P[x_, n_] := P[x, n] = (2*n + a0 + 1 - x)*P[x, n - 1]/(n + 1) - n*P[x, n - 2]/(n + 1); Table[ExpandAll[(n + 2)!*P[x, n]/2], {n, 0, 10}]; a = Table[CoefficientList[(n + 2)!*P[x, n]/2, x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A021009.
Sequence in context: A065500 A120341 A094357 this_sequence A030417 A123979 A013583
Adjacent sequences: A136529 A136530 A136531 this_sequence A136533 A136534 A136535
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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 23 2008
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