cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A157867 Denominator of Bernoulli(n, 1/5).

Original entry on oeis.org

1, 10, 150, 125, 3750, 3125, 656250, 78125, 2343750, 1953125, 644531250, 48828125, 133300781250, 1220703125, 36621093750, 30517578125, 15563964843750, 762939453125, 3044128417968750, 19073486328125, 6294250488281250
Offset: 0

Views

Author

N. J. A. Sloane, Nov 08 2009

Keywords

Links

Crossrefs

For numerators see A157866.

Programs

  • Mathematica
    Table[Denominator[BernoulliB[n, 1/5]], {n, 0, 50}] (* Vincenzo Librandi, Mar 19 2014 *)
  • PARI
    a(n)=denominator(subst(bernpol(n, x), x, 1/5)); \\ Michel Marcus, Jul 06 2017

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

Original entry on oeis.org

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

Views

Author

Wolfdieter Lang, Jul 05 2017

Keywords

Comments

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

Links

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

A157883 Numerator of Bernoulli(n, 2/5).

Original entry on oeis.org

1, -1, -11, 3, 91, -43, -12347, 1183, 62851, -54423, -39448591, 3799763, 27287144401, -375591203, -34562009741, 49954996743, 89299092717107, -8604866798383, -135379643536733633, 1863607913992123, 2694379428323830241, -495661415843787963, -1648224141847799919403
Offset: 0

Views

Author

N. J. A. Sloane, Nov 08 2009

Keywords

Comments

From Wolfdieter Lang, Jul 05 2017: (Start)
a(n) gives also the numerators of the generalized Bernoulli numbers B[5,2](n) = 5^n*Bernoulli(n, 2/5) with the Bernoulli polynomials B(n, x) = Bernoulli(n, x) from A196838/A196839 or A053382/A053383. For the denominators see A288872(n) = A157867(n)/5^n. See a comment under A157866 for B[d,a](n).
(-1)^n*a(n) gives the numerators of the generalized Bernoulli numbers B[5,3](n); the denominators are A288872(n).
(End)

Links

Crossrefs

For denominators see A157867.
Cf. A288872.

Programs

  • Mathematica
    Table[Numerator[BernoulliB[n, 2/5]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)
  • PARI
    a(n) = numerator(subst(bernpol(n, x), x, 2/5)); \\ Michel Marcus, Jul 06 2017
  • Python
    from sympy import bernoulli, Integer
def a(n): return bernoulli(n, Integer(2)/5).numerator
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 06 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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