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Search: id:A122057
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| A122057 |
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A Legendre based recureence sequence:a(n) = ((-2*n - 1) + (4*n + 2)*x)/(n + 1)*a(n - 1) - (n/(n + 1))*a[n - 2]: x=1. |
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+0
1
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| 0, -2, -14, -94, -684, -5508, -49104, -482256, -5185440, -60668640, -767940480, -10462227840, -152698210560, -2377651449600, -39350097561600, -689874448435200, -12773427499929600, -249097496204390400, -5103595024496640000, -109608397522606080000
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964, 9th Printing (1970), pp. 782
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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FORMULA
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a(n) = ((-2*n - 1) + (4*n + 2)*x)/(n + 1)*a(n - 1) - (n/(n + 1))*a[n - 2]: x=1 output=a(n)*(n+1)!
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MAPLE
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a:=n->-sum(n!/k, k=3..n): seq(a(n), n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 22 2008
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MATHEMATICA
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x = 1; a[0] = 1/2; a[1] = 0; a[n_] := a[n] = ((-2*n - 1) + (4*n + 2)*x)/(n + 1)*a[n - 1] - (n/(n + 1))*a[n - 2] Table[a[n]*(n + 1)!, {n, 1, 30}]
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CROSSREFS
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Sequence in context: A033169 A090410 A066052 this_sequence A141146 A109808 A037516
Adjacent sequences: A122054 A122055 A122056 this_sequence A122058 A122059 A122060
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KEYWORD
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sign,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 14 2006
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EXTENSIONS
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If all terms are really negative, sequence should probably be negated. - njas, Oct 01 2006
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