A083687 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.
1, 5, 7, 761, 671, 4572347, 1171733, 518413759, 32956355893, 1949885751497, 21495895979, 63715389517501781, 22630025105469577, 36899945775958445129, 517210776697519633301437, 4518133367201930332907311663
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..260
- Ira Gessel, On Miki's identity for Bernoulli numbers J. Number Theory 110 (2005), no. 1, 75-82.
Crossrefs
Cf. A083688.
Programs
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Mathematica
Table[ BernoulliB[2n] * HarmonicNumber[2n] / n // Numerator // Abs, {n, 1, 16}] (* Jean-François Alcover, Mar 24 2015 *) -
PARI
a(n)=numerator((-1)^(n+1)*bernfrac(2*n)*sum(k=1,2*n,1/k)/n)
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Python
from sympy import bernoulli, harmonic, numer def a(n): return numer(bernoulli(2 * n) * harmonic(2 * n) * (-1)**(n + 1) / n) [a(n) for n in range(1, 31)] # Indranil Ghosh, Aug 04 2017
Formula
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)))