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 A122057 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. 0
 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; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = (n+1)*a(n-1) - n!..3*0-2 =-2, 4*(-2)-6=-14, 5*(-14)-24=-94, ... - Gary Detlefs, May 22 2010 It appears that a(n) is a function of the harmonic numbers. - Gary Detlefs, Jul 15 2010 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 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]. 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_{k=3..n+2} -1/k with offset 0. - Gary Detlefs, Jul 15 2010 MAPLE a:=n->-sum(n!/k, k=3..n): seq(a(n), n=2..21); # Zerinvary Lajos, Jan 22 2008 f:=n->(n+2)!*sum(-1/k, k=3..n+2):seq(f(n), n=0..20); # Gary Detlefs, Jul 15 2010 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}] CROSSREFS Sequence in context: A033169 A090410 A066052 * A164891 A141146 A267913 Adjacent sequences:  A122054 A122055 A122056 * A122058 A122059 A122060 KEYWORD sign,uned AUTHOR Roger L. Bagula, Sep 14 2006 EXTENSIONS If all terms are really negative, sequence should probably be negated. - N. J. A. Sloane, Oct 01 2006 STATUS approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)