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Search: id:A136533
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| A136533 |
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Coefficients of Laguerre recursive polynomials with an (n+2)!/2 multiplication factor, and alpha=a0 =0 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, 3, -3, 12, -24, 4, 60, -180, 65, -5, 360, -1440, 822, -132, 6, 2520, -12600, 9954, -2478, 231, -7, 20160, -120960, 122832, -41856, 5976, -368, 8, 181440, -1270080, 1581768, -688392, 133380, -12492, 549, -9, 1814400, -14515200, 21462480, -11412000, 2806200, -354720, 23610, -780, 10, 19958400
(list; table; graph; listen)
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OFFSET
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1,2
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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, 0, -8, -60, -384, -2380, -14208, -73836, -176000, 3824964, 104573760}
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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=0; 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},
{3, -3},
{12, -24, 4},
{60, -180,65, -5},
{360, -1440, 822, -132, 6},
{2520, -12600, 9954, -2478, 231, -7},
{20160, -120960,122832, -41856, 5976, -368, 8},
{181440, -1270080, 1581768, -688392, 133380, -12492, 549, -9},
{1814400, -14515200, 21462480, -11412000, 2806200, -354720, 23610, -780, 10}, {19958400, -179625600, 307937520, -193968720, 57998160, -9263760, 829290, -41382, 1067, -11},
{239500800, -2395008000, 4675026240, -3410138880, 1203543360, -232928640, 26271000, -1759104, 68388, -1416, 12}
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MATHEMATICA
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a0 = 0; 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.
Adjacent sequences: A136530 A136531 A136532 this_sequence A136534 A136535 A136536
Sequence in context: A078666 A006804 A052533 this_sequence A097342 A025236 A014432
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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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