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%I #17 Mar 19 2017 05:51:08
%S 1,1,-6049,220961,-94911125449,671622173,16973944396387813,
%T -46178297272884601,648295260682210793677,58263405848420369,
%U -12621473417377804010947847693,30937406138704675992342953,117859933384302464321297008587517702333
%N Numerators of poly-Bernoulli numbers B_n^(k) with k = 8.
%H Seiichi Manyama, <a href="/A283932/b283932.txt">Table of n, a(n) for n = 0..249</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Poly-Bernoulli_number">Poly-Bernoulli number</a>
%e B_0^(8) = 1, B_1^(8) = 1/256, B_2^(8) = -6049/1679616, B_3^(8) = 220961/71663616, ...
%t B[n_]:= Sum[((-1)^(m + n))*m!*StirlingS2[n, m] * (m + 1)^(-8), {m, 0, n}]; Table[Numerator[B[n]], {n, 0, 15}] (* _Indranil Ghosh_, Mar 18 2017 *)
%o (PARI) B(n) = sum(m=0, n, ((-1)^(m + n)) * m! * stirling(n, m, 2) * (m + 1)^(-8)); for(n=0, 15, print1(numerator(B(n)), ", ")) \\ _Indranil Ghosh_, Mar 18 2017
%Y Cf. A283933.
%K sign,frac
%O 0,3
%A _Seiichi Manyama_, Mar 18 2017
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