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A083687
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Numerator of B(2n)*H(2n)/n*(-1)^(n+1) where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.
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3
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1, 5, 7, 761, 671, 4572347, 1171733, 518413759, 32956355893, 1949885751497, 21495895979, 63715389517501781, 22630025105469577, 36899945775958445129, 517210776697519633301437, 4518133367201930332907311663
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OFFSET
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1,2
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LINKS
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FORMULA
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Miki's identity : B(n)*H(n)*(2/n) = sum(i=2, n-2, B(i)/i*B(n-i)/(n-i)*(1-C(n, i)))
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MATHEMATICA
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Table[ BernoulliB[2n] * HarmonicNumber[2n] / n // Numerator // Abs, {n, 1, 16}] (* Jean-François Alcover, Mar 24 2015 *)
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PROG
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(PARI) a(n)=numerator((-1)^(n+1)*bernfrac(2*n)*sum(k=1, 2*n, 1/k)/n)
(Python)
from sympy import bernoulli, harmonic, numer
def a(n):
return numer(bernoulli(2 * n) * harmonic(2 * n) * (-1)**(n + 1) / n)
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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