%I #41 May 04 2020 14:08:09
%S 4,144,360,33600,15120,34927200,2162160,172972800,1543782240,
%T 10242872640,10346336,2338727174784,53542288800,4818805992000,
%U 3228118134040800,1178332991611776000,78765574305600,12256711017694416000,2914326249307200,3205758874237920000,358462128664785600
%N Denominator of B(2n)*H(2n)/n where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.
%C B(2n) is negative for even n, but this does not affect the denominator. - _M. F. Hasler_, Dec 24 2013
%H Seiichi Manyama, <a href="/A083688/b083688.txt">Table of n, a(n) for n = 1..500</a> (terms 1..50 from M. F. Hasler)
%H Ira Gessel, <a href="https://doi.org/10.1016/j.jnt.2003.08.010">On Miki's identity for Bernoulli numbers</a> J. Number Theory 110 (2005), no. 1, 75-82.
%F 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)))
%t Denominator[Table[(BernoulliB[2n]HarmonicNumber[2n])/(n (-1)^(n+1)),{n,20}]] (* _Harvey P. Dale_, Jun 25 2013 *)
%o (PARI) a(n)=denominator(bernfrac(2*n)*sum(k=1,2*n,1/k)/n)
%o (Python)
%o from sympy import bernoulli, harmonic
%o def a(n): return (bernoulli(2*n) * harmonic(2*n) / n).denominator()
%o print([a(n) for n in range(1, 22)]) # _Indranil Ghosh_, Aug 04 2017
%Y Cf. A083687.
%K frac,nonn
%O 1,1
%A _Benoit Cloitre_, Jun 15 2003