login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288872 Denominators for generalized Bernoulli numbers B[5,j](n), for j=1..4, n >= 0. 3

%I #26 May 05 2020 15:30:59

%S 1,2,6,1,6,1,42,1,6,1,66,1,546,1,6,1,102,1,798,1,66,1,138,1,546,1,6,1,

%T 174,1,14322,1,102,1,6,1,383838,1,6,1,2706,1,1806,1,138,1,282,1,9282,

%U 1,66,1,318,1,798,1,174,1,354,1,11357346,1,6,1,102,1,64722,1,6,1,4686

%N Denominators for generalized Bernoulli numbers B[5,j](n), for j=1..4, n >= 0.

%C See, e.g., A157871 for details on B[d,a](n) with gcd(d,a) = 1.

%H Antti Karttunen, <a href="/A288872/b288872.txt">Table of n, a(n) for n = 0..10101</a>

%H Wolfdieter Lang, <a href="https://arxiv.org/abs/1707.04451">On Sums of Powers of Arithmetic Progressions, and Generalized Stirling, Eulerian and Bernoulli numbers</a>, arXiv:1707.04451 [math.NT], 2017.

%t Table[Denominator[BernoulliB[n, 1/5]]/5^n, {n, 0, 70}] (* _Jean-François Alcover_, Sep 24 2018, from PARI *)

%o (PARI) a(n)=denominator(subst(bernpol(n, x), x, 1/5))/5^n; \\ _Michel Marcus_, Jul 06 2017

%o (Python)

%o from sympy import bernoulli

%o def a(n): return bernoulli(n, 1/Integer(5)).denominator()//(5**n)

%o print([a(n) for n in range(41)]) # _Indranil Ghosh_, Jul 06 2017

%Y Cf. A027642 (denominators B[1,0]), A141459 (denominators B[2,1]), A285068 (denominators B[3,1] and B[3,2]), A141459 (denominators B[4,1] and B[4,3]).

%Y For the numerators of B[5,j](n), for j=1..4, see A157866(n), A157883(n), (-1)^n*A157883(n), (-1)^n*A157866(n), respectively.

%Y Cf. A157871.

%K nonn,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 05 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)