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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

Table of n, a(n) for n=1..20.

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.)