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A157799
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Numerator of Bernoulli(n, 1/3).
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3
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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
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OFFSET
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0,5
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Table[Numerator[BernoulliB[n, 1/3]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)
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PROG
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(Python)
from sympy import bernoulli, Integer
def a(n): return bernoulli(n, 1/Integer(3)).numerator() # Indranil Ghosh, May 01 2017
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CROSSREFS
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KEYWORD
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sign,easy,frac
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AUTHOR
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STATUS
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approved
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