A157799 Numerator of Bernoulli(n, 1/3).

1, -1, -1, 1, 13, -5, -121, 49, 1093, -809, -49205, 20317, 61203943, -722813, -5580127, 34607305, 25949996501, -2145998417, -2832495743227, 167317266613, 101471818419863, -16020403322021, -4469253897850313, 1848020950359841, 11126033443528968583, -252778977216700025

Offset: 0

Author

N. J. A. Sloane, Nov 08 2009

Keywords

• sign
• easy
• frac

Comments

This sequence gives also the numerators of the generalized Bernoulli numbers B[3,1](n) = 3^n*Bernoulli(n, 1/3) with denominators given by A285068. See the formula and example section there for the rationals. The numbers B[3,2](n) = 3^n*Bernoulli(n, 2/3) = (-1)^n*B[3,1](n) have numerators (-1)^n*a(n) and denominators A285068 (proof from the e.g.f.s). - Wolfdieter Lang, Apr 28 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..250

Crossrefs

For denominators see A157800, A285068.

Programs

Mathematica

Table[Numerator[BernoulliB[n, 1/3]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)

PARI

a(n) = my(x=1/3); numerator(eval(bernpol(n))); \\ Ruud H.G. van Tol, May 10 2024

Python

from sympy import bernoulli, Integer
def a(n): return bernoulli(n, 1/Integer(3)).numerator # Indranil Ghosh, May 01 2017