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%I #14 Jul 10 2017 04:18:47
%S 1,-3,1,6,-29,-74,4537,1946,-23789,-88434,15034541,6154786,
%T -10417027559,-607884394,13199705071,80834386026,-34108052679853,
%U -13923204233954,51709981061257363,3015393801263666,-1029159167703800359,-801997872697905114,629565265428734672873
%N Numerator of Bernoulli(n, 1/5).
%C From _Wolfdieter Lang_, Jul 05 2017: (Start)
%C a(n) gives also the numerators of the generalized Bernoulli numbers B[5,1](n) = 5^n*B(n, 1/5) 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.
%C (-1)^n*a(n) gives the numerators of the generalized Bernoulli numbers B[5,4](n). The denominators are also A288872(n).
%C The generalized Bernoulli numbers B[d,a](n), for d >= 1, a >= 0, with gcd(d, a) = 1 are defined in terms of generalized Stirling2 numbers by B[d,a](n) = Sum_{k=0..n} ((-1)^k / (k+1))*S2[d,a](n, k)*k!, n >= 0. See A285061 for more details.
%C (End)
%H Vincenzo Librandi, <a href="/A157866/b157866.txt">Table of n, a(n) for n = 0..250</a>
%t Table[Numerator[BernoulliB[n, 1/5]], {n, 0, 50}] (* _Vincenzo Librandi_, Mar 16 2014 *)
%o (PARI) a(n)=numerator(subst(bernpol(n, x), x, 1/5)); \\ _Michel Marcus_, Jul 06 2017
%Y For denominators see A157867, and also A288872.
%Y Cf. A053382/A053383, A196838/A196839, A285061.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 08 2009