A083688 Denominator of B(2n)*H(2n)/n where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.

4, 144, 360, 33600, 15120, 34927200, 2162160, 172972800, 1543782240, 10242872640, 10346336, 2338727174784, 53542288800, 4818805992000, 3228118134040800, 1178332991611776000, 78765574305600, 12256711017694416000, 2914326249307200, 3205758874237920000, 358462128664785600

Offset

1,1

Comments

B(2n) is negative for even n, but this does not affect the denominator. - M. F. Hasler, Dec 24 2013

Links

Seiichi Manyama, Table of n, a(n) for n = 1..500 (terms 1..50 from M. F. Hasler)

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

Denominator[Table[(BernoulliB[2n]HarmonicNumber[2n])/(n (-1)^(n+1)), {n, 20}]] (* Harvey P. Dale, Jun 25 2013 *)

Prog

(PARI) a(n)=denominator(bernfrac(2*n)*sum(k=1, 2*n, 1/k)/n)
(Python)
from sympy import bernoulli, harmonic
def a(n): return (bernoulli(2*n) * harmonic(2*n) / n).denominator()
print([a(n) for n in range(1, 22)]) # Indranil Ghosh, Aug 04 2017

Crossrefs

Cf. A083687.

Sequence in context: A122422 A307703 A277948 * A053899 A058414 A053891

Adjacent sequences: A083685 A083686 A083687 * A083689 A083690 A083691

Keyword

frac,nonn

Author

Benoit Cloitre, Jun 15 2003

Status

approved