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%I A157799 #25 May 10 2024 16:52:01
%S A157799 1,-1,-1,1,13,-5,-121,49,1093,-809,-49205,20317,61203943,-722813,
%T A157799 -5580127,34607305,25949996501,-2145998417,-2832495743227,
%U A157799 167317266613,101471818419863,-16020403322021,-4469253897850313,1848020950359841,11126033443528968583,-252778977216700025
%N A157799 Numerator of Bernoulli(n, 1/3).
%C A157799 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
%H A157799 Vincenzo Librandi, <a href="/A157799/b157799.txt">Table of n, a(n) for n = 0..250</a>
%t A157799 Table[Numerator[BernoulliB[n, 1/3]], {n, 0, 50}] (* _Vincenzo Librandi_, Mar 16 2014 *)
%o A157799 (Python)
%o A157799 from sympy import bernoulli, Integer
%o A157799 def a(n): return bernoulli(n, 1/Integer(3)).numerator() # _Indranil Ghosh_, May 01 2017
%o A157799 (PARI) a(n) = my(x=1/3); numerator(eval(bernpol(n))); \\ _Ruud H.G. van Tol_, May 10 2024
%Y A157799 For denominators see A157800, A285068.
%K A157799 sign,easy,frac
%O A157799 0,5
%A A157799 _N. J. A. Sloane_, Nov 08 2009

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