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Search: id:A137338
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| A137338 |
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Triangular sequence from recursive Charlier polynomials:a=1; Ca(x, n) = (x - (n - 1) - a)*Ca(x, n - 1) - a*n*Ca(x, n - 2). |
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1
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| 1, -1, 1, 0, -3, 1, 3, 6, -6, 1, -12, -9, 26, -10, 1, 45, 3, -109, 71, -15, 1, -198, 81, 501, -475, 155, -21, 1, 1071, -786, -2663, 3329, -1455, 295, -28, 1, -6984, 6711, 16510, -25495, 13729, -3647, 511, -36, 1, 53217, -60309, -117912, 216004, -135961, 43897, -7994, 826, -45, 1, -462330, 589197, 953711
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 0, -2, 4, -4, -4, 44, -236, 1300, -8276, 61484}
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REFERENCES
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M. Dunster, Uniform asymptotic expansions for Charlier polynomials, J. Approx. Theory, 112 (2001) pp. 93 - 133 http : // www - rohan.sdsu.edu/~dunster/Charlier.pdf
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FORMULA
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a=1; Ca(x, n) = (x - (n - 1) - a)*Ca(x, n - 1) - a*n*Ca(x, n - 2);
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EXAMPLE
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{1},
{-1, 1},
{0, -3, 1},
{3, 6, -6,1},
{-12, -9, 26, -10, 1},
{45, 3, -109, 71, -15, 1},
{-198, 81, 501, -475, 155, -21, 1},
{1071, -786, -2663, 3329, -1455, 295, -28, 1},
{-6984, 6711, 16510, -25495, 13729, -3647, 511, -36, 1},
{53217, -60309, -117912, 216004, -135961, 43897, -7994, 826, -45, 1},
{-462330, 589197, 953711, -2023002, 1438324, -538461, 118727, -15894, 1266, -55, 1}
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MATHEMATICA
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Ca[x, -1] = 0; Ca[x, 0] = 1; Ca[x_, n_] := Ca[x, n] = (x - (n - 1) - 1)*Ca[x, n - 1] - n*Ca[x, n - 2]; Table[ExpandAll[Ca[x, n]], {n, 0, 10}]; a = Table[CoefficientList[Ca[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137335 A137336 A137337 this_sequence A137339 A137340 A137341
Sequence in context: A114159 A033789 A109532 this_sequence A058659 A053642 A122507
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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), Apr 07 2008
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