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 A122057 a(n) = (n+1)! * (H(n+1) - H(2)), where H(n) are the harmonic numbers. 1
 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 Former title (corrected): A Legendre-based recurrence sequence. Let b(n) = ((4*n+2)*x -(2*n+1) )/(n+1)*b(n-1) - (n/(n+1))*b(n-2), where x=1, then a(n) = (n+1)!*b(n)/6. - G. C. Greubel, Oct 03 2019 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 G. C. Greubel, Table of n, a(n) for n = 1..445 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 Let b(n) = ((-2*n-1) +(4*n+2)*x)/(n+1)*b(n-1) - (n/(n+1))*b(n-2) with x=1, then a(n) = b(n)*(n+1)!/6. a(n) = (n+1)! * Sum_{k=3..n+1} 1/k. - Gary Detlefs, Jul 15 2010 MAPLE a:=n-> (n+1)!*add(1/k, k=3..n+1): seq(a(n), n=1..30); # Gary Detlefs, Jul 15 2010 MATHEMATICA x=1; b[1]:=0; b[2]:=2; b[n_]:= b[n]= ((-2*n-1) +(4*n+2)*x)/(n+1)*b[n-1] - (n/(n+1))*b[n-2]; Table[b[n]*(n+1)!/6, {n, 30}] Table[(n+1)!*(HarmonicNumber[n+1] - 3/2), {n, 30}] (* G. C. Greubel, Oct 03 2019 *) PROG (PARI) vector(30, n, (n+1)!*(sum(k=1, n+1, 1/k) - 3/2) ) \\ G. C. Greubel, Oct 03 2019 (Magma) [Factorial(n+1)*(HarmonicNumber(n+1) - 3/2): n in [1..30]]; // G. C. Greubel, Oct 03 2019 (Sage) [factorial(n+1)*(harmonic_number(n+1) - 3/2) for n in (1..30)] # G. C. Greubel, Oct 03 2019 (GAP) List([1..30], n-> Factorial(n+1)*(Sum([1..n+1], k-> 1/k) - 3/2) ); # G. C. Greubel, Oct 03 2019 CROSSREFS Cf. A001008, A002805. Sequence in context: A033169 A090410 A066052 * A164891 A141146 A267913 Adjacent sequences: A122054 A122055 A122056 * A122058 A122059 A122060 KEYWORD nonn 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 Negated terms and edited by G. C. Greubel, Oct 03 2019 STATUS approved

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Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)