A050932 - OEIS

%I #30 Apr 02 2021 17:57:56

%S 1,1,2,1,6,1,6,1,10,1,6,1,210,1,2,1,30,1,42,1,110,1,6,1,546,1,2,1,30,

%T 1,462,1,170,1,6,1,51870,1,2,1,330,1,42,1,46,1,6,1,6630,1,22,1,30,1,

%U 798,1,290,1,6,1,930930,1,2,1,102,1,966,1,10,1,66,1,1919190

%N Denominator of (n+1)*Bernoulli(n).

%C Apparently a(n) = denominator(Sum_{k=0..n-1} (-1)^(n-k+1)*E1(n, k+1)/binomial(n, k+1)), where E1(n, k) denotes the first-order Eulerian numbers A123125. - _Peter Luschny_, Feb 17 2021

%H Antti Karttunen, <a href="/A050932/b050932.txt">Table of n, a(n) for n = 0..20000</a> (terms 0..200 from N. J. A. Sloane)

%H M. Kaneko, <a href="https://doi.org/10.3792/pjaa.71.192">A recurrence formula for the Bernoulli numbers</a>, Proc. Japan Acad., 71 A (1995), 192-193.

%H S. C. Woon, <a href="http://www.jstor.org/stable/2691054">A tree for generating Bernoulli numbers</a>, Math. Mag., 70 (1997), 51-56.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%t Denominator/@Table[(n+1)BernoulliB[n],{n,0,80}] (* _Harvey P. Dale_, May 19 2011 *)

%o (Haskell)

%o a050932 n = a050932_list !! n

%o a050932_list = 1 : map (denominator . sum) (zipWith (zipWith (%))

%o    (zipWith (map . (*)) (drop 2 a000142_list) a242179_tabf) a106831_tabf)

%o -- _Reinhard Zumkeller_, Jul 04 2014

%o (PARI) a(n)=denominator(bernfrac(n)*(n+1)) \\ _Charles R Greathouse IV_, Feb 07 2017

%o (Python)

%o from sympy import bernoulli, gcd

%o def A050932(n):

%o     q = bernoulli(n).q

%o     return q//gcd(q,n+1) # _Chai Wah Wu_, Apr 02 2021

%Y Cf. A050925, A000367/A002445, A027641/A027642, A002882, A003245, A127187, A127188, A242179, A106831, A000142, A123125.

%K nonn,frac,nice,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 30 1999