A283933 - OEIS

%I #17 Mar 19 2017 01:16:31

%S 1,256,1679616,71663616,41990400000000,622080000000,

%T 48413259982080000000,29509034655744000000,403351617450700800000000,

%U 102438506019225600000,2882066712209076538460160000000,6654122279270595182592000000

%N Denominators of poly-Bernoulli numbers B_n^(k) with k = 8.

%H Seiichi Manyama, <a href="/A283933/b283933.txt">Table of n, a(n) for n = 0..351</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[Denominator[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));

%o for(n=0, 15, print1(denominator(B(n)), ", ")) \\ _Indranil Ghosh_, Mar 18 2017

%Y Cf. A283932.

%K nonn,frac

%O 0,2

%A _Seiichi Manyama_, Mar 18 2017