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A122057
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A Legendre based recurrence 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
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = (n+1)*a(n-1) - n!..3*0-2 =-2, 4*(-2)-6=-14,5*(-14)-24=-94... [From Gary Detlefs (gdetlefs(AT)aol.com), May 22 2010]
It appears that a(n) is a function of the harmonic numbers [From Gary Detlefs (gdetlefs(AT)aol.com), Jul 15 2010]
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REFERENCES
| 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
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
| 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)!
a(n) = (n+2)!*sum(-1/k,k=3..n+2), with offset 0 [From Gary Detlefs (gdetlefs(AT)aol.com), Jul 15 2010]
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MAPLE
| a:=n->-sum(n!/k, k=3..n): seq(a(n), n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 22 2008
f:=n->(n+2)!*sum(-1/k, k=3..n+2):seq(f(n), n=0..20); [From Gary Detlefs (gdetlefs(AT)aol.com), Jul 15 2010]
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MATHEMATICA
| 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
| Sequence in context: A033169 A090410 A066052 * A164891 A141146 A204699
Adjacent sequences: A122054 A122055 A122056 * A122058 A122059 A122060
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KEYWORD
| sign,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 14 2006
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EXTENSIONS
| If all terms are really negative, sequence should probably be negated. - N. J. A. Sloane (njas(AT)research.att.com), Oct 01 2006
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