A283921 Numerators of poly-Bernoulli numbers B_n^(k) with k=5.

1, 1, -179, 515, -216383, -183781, 4644828197, 153375307, -371224706507, 959290541, 575134377343021, -14855426650259, -29106619674489691525729, 225456132288901603, 263567702701300558681, -355061945309358701, -1432477558547377054456843733

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..345

Wikipedia, Poly-Bernoulli number

Example

B_0^(5) = 1, B_1^(5) = 1/32, B_2^(5) = -179/7776, B_3^(5) = 515/41472, ...

Mathematica

B[n_]:= Sum[((-1)^(m + n)) * m! * StirlingS2[n, m] * (m + 1)^(-5), {m, 0, n}]; Table[Numerator[B[n]], {n, 0, 16}] (* Indranil Ghosh, Mar 18 2017 *)

Prog

(PARI) B(n) = sum(m=0, n, ((-1)^(m + n)) * m! * stirling(n, m, 2) * (m + 1)^(-5));
for(n=0, 16, print1(numerator(B(n)), ", ")) \\ Indranil Ghosh, Mar 18 2017

Crossrefs

Cf. A283922.

Sequence in context: A162163 A062651 A142611 * A120821 A255096 A253627

Adjacent sequences: A283918 A283919 A283920 * A283922 A283923 A283924

Keyword

sign,frac

Author

Seiichi Manyama, Mar 18 2017

Status

approved