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A129814
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a(n) = Bernoulli(n) * (n+1)!.
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8
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1, -1, 1, 0, -4, 0, 120, 0, -12096, 0, 3024000, 0, -1576143360, 0, 1525620096000, 0, -2522591034163200, 0, 6686974460694528000, 0, -27033456071346536448000, 0, 160078872315904478576640000, 0, -1342964491649083924630732800000, 0
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OFFSET
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0,5
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COMMENTS
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2*a(n) = (-1)^n*A159749(n, 0) for n >= 0. (End)
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LINKS
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FORMULA
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E.g.f.: -2 x - psi_2(1/x) / x^2, where psi_n(z) is the polygamma function, psi_n(z) = (d/dz)^{n+1} log(Gamma(z)). - Vladimir Reshetnikov, Apr 24 2013
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MATHEMATICA
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Table[BernoulliB[n](n+1)!, {n, 0, 30}] (* Harvey P. Dale, Jan 18 2013 *)
Table[SeriesCoefficient[-2 x - PolyGamma[2, 1/x] / x^2, {x, 0, n}, Assumptions -> x > 0] n!, {n, 0, 30}] (* Vladimir Reshetnikov, Apr 24 2013 *)
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PROG
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(PARI) {for(n=0, 25, print1(bernfrac(n)*(n+1)!, ", "))}
(PARI) {a(n) = if( n<0, 0, (n + 1)! * bernfrac( n))} /* Michael Somos, Mar 29 2011 */
(Magma) [Bernoulli(n) * Factorial(n+1): n in [0..100]]; // Vincenzo Librandi, Mar 29 2011
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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