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

1,2

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.

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)))

Mathematica

Table[ BernoulliB[2n] * HarmonicNumber[2n] / n // Numerator // Abs, {n, 1, 16}] (* Jean-François Alcover, Mar 24 2015 *)

Prog

(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)
[a(n) for n in range(1, 31)]  # Indranil Ghosh, Aug 04 2017

Crossrefs

Cf. A083688.

Sequence in context: A020467 A089344 A114363 * A101829 A056252 A274774

Adjacent sequences: A083684 A083685 A083686 * A083688 A083689 A083690

Keyword

frac,nonn

Author

Benoit Cloitre, Jun 15 2003

Status

approved