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A137384
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A triangular sequence of coefficients of a modified Neumann polynomial recursion: No(x, n) = (2*n/x)*No(x, n - 1) + (-n/(n - 2))*No( x, n - 2) + Ceiling[(2*(n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x; weighted by 2*x^(n + 1).
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0
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2, 2, 8, 0, 2, 48, 0, 6, 384, 0, 32, 0, -10, 3840, 0, 240, 0, -110, 46080, 0, 2304, 0, -1368, 0, 21, 645120, 0, 26880, 0, -19488, 0, 448, 10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32, 185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152, 3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46
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OFFSET
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1,1
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COMMENTS
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Row sums are: {2, 2, 10, 54, 406, 3970, 47037, 652960, 10384640, 186084000, 3708699206};
The ceiling function and 2*x^(n+1) were used to give integers.
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REFERENCES
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Weisstein, Eric W. "Neumann Polynomial." http://mathworld.wolfram.com/NeumannPolynomial.html
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LINKS
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Table of n, a(n) for n=1..61.
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FORMULA
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No(x, n) = (2*n/x)*No(x, n - 1) + (-n/(n - 2))*No( x, n - 2) + Ceiling[(2*(n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x; weighted by 2*x^(n + 1).
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EXAMPLE
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{2},
{2},
{8, 0, 2},
{48, 0, 6},
{384, 0, 32, 0, -10},
{3840, 0, 240, 0, -110},
{46080, 0, 2304, 0, -1368, 0, 21},
{645120, 0, 26880, 0, -19488,0, 448},
{10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32},
{185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152},
{3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46}
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MATHEMATICA
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Clear[No, a] No[x, -1] = 0; No[x, 0] = 1/x; No[x, 1] = 1/x^2; No[x, 2] = (x^2 + 4)/x^3; No[x_, n_] := No[x, n] = (2*n/x)*No[ x, n - 1] + (-n/(n - 2))*No[x, n - 2] + Ceiling[(2*( n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x; Table[ExpandAll[2*x^(n + 1)*No[x, n]], {n, 0, 10}]; a = Table[CoefficientList[2*x^(n + 1)*No[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A248237 A139523 A359057 * A051148 A102645 A344734
Adjacent sequences: A137381 A137382 A137383 * A137385 A137386 A137387
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula, Apr 09 2008
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STATUS
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approved
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