A283924 - OEIS

%I #15 Mar 18 2017 08:34:10

%S 1,64,46656,497664,11664000000,518400000,274451587200000,

%T 41821194240000,63515938752000000,403275801600000,

%U 3750745332381062400000,8659729483130880000,115208108444831203593792000000,60895775359471852800000,189903475458512972956800000

%N Denominators of poly-Bernoulli numbers B_n^(k) with k=6.

%H Seiichi Manyama, <a href="/A283924/b283924.txt">Table of n, a(n) for n = 0..479</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Poly-Bernoulli_number">Poly-Bernoulli number</a>

%e B_0^(6) = 1, B_1^(6) = 1/64, B_2^(6) = -601/46656, B_3^(6) = 4409/497664, ...

%t B[n_]:= Sum[((-1)^(m + n))*m!*StirlingS2[n, m] * (m + 1)^(-6), {m, 0, n}];

%t 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)^(-6));

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

%Y Cf. A283923.

%K nonn,frac

%O 0,2

%A _Seiichi Manyama_, Mar 18 2017