OFFSET
0,5
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
MATHEMATICA
Table[Numerator[BernoulliB[n, 1/3]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)
PROG
(Python)
from sympy import bernoulli, Integer
def a(n): return bernoulli(n, 1/Integer(3)).numerator() # Indranil Ghosh, May 01 2017
(PARI) a(n) = my(x=1/3); numerator(eval(bernpol(n))); \\ Ruud H.G. van Tol, May 10 2024
CROSSREFS
KEYWORD
sign,easy,frac
AUTHOR
N. J. A. Sloane, Nov 08 2009
STATUS
approved