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A288872 Denominators for generalized Bernoulli numbers B[5,j](n), for j=1..4, n >= 0.

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%I A288872 #29 Jun 27 2025 15:09:08
%S A288872 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 A288872 174,1,14322,1,102,1,6,1,383838,1,6,1,2706,1,1806,1,138,1,282,1,9282,
%U A288872 1,66,1,318,1,798,1,174,1,354,1,11357346,1,6,1,102,1,64722,1,6,1,4686
%N A288872 Denominators for generalized Bernoulli numbers B[5,j](n), for j=1..4, n >= 0.
%C A288872 See, e.g., A157871 for details on B[d,a](n) with gcd(d,a) = 1.
%H A288872 Antti Karttunen, <a href="/A288872/b288872.txt">Table of n, a(n) for n = 0..10101</a>
%H A288872 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 A288872 Table[Denominator[BernoulliB[n, 1/5]]/5^n, {n, 0, 70}] (* _Jean-François Alcover_, Sep 24 2018, from PARI *)
%o A288872 (PARI) a(n)=denominator(subst(bernpol(n, x), x, 1/5))/5^n; \\ _Michel Marcus_, Jul 06 2017
%o A288872 (Python)
%o A288872 from sympy import bernoulli
%o A288872 def a(n): return bernoulli(n, 1/Integer(5)).denominator//(5**n)
%o A288872 print([a(n) for n in range(41)]) # _Indranil Ghosh_, Jul 06 2017
%Y A288872 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 A288872 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 A288872 Cf. A157871.
%K A288872 nonn,frac
%O A288872 0,2
%A A288872 _Wolfdieter Lang_, Jul 05 2017