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

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, 174, 1, 14322, 1, 102, 1, 6, 1, 383838, 1, 6, 1, 2706, 1, 1806, 1, 138, 1, 282, 1, 9282, 1, 66, 1, 318, 1, 798, 1, 174, 1, 354, 1, 11357346, 1, 6, 1, 102, 1, 64722, 1, 6, 1, 4686

Offset: 0

Author

Wolfdieter Lang, Jul 05 2017

Keywords

• nonn
• frac

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10101
• Wolfdieter Lang, On Sums of Powers of Arithmetic Progressions, and Generalized Stirling, Eulerian and Bernoulli numbers, arXiv:1707.04451 [math.NT], 2017.

Crossrefs

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]).

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.

Cf. A157871.

Programs

Mathematica

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

PARI

a(n)=denominator(subst(bernpol(n, x), x, 1/5))/5^n; \\ Michel Marcus, Jul 06 2017

Python

from sympy import bernoulli
def a(n): return bernoulli(n, 1/Integer(5)).denominator//(5**n)
print([a(n) for n in range(41)]) # Indranil Ghosh, Jul 06 2017