A027646 Denominators of poly-Bernoulli numbers B_n^(k) with k=3.

1, 8, 216, 288, 54000, 7200, 3704400, 35280, 7938000, 16800, 78262800, 304920, 4923832914000, 535392, 32464832400, 240240, 265832869302000, 2082880800, 50052680603125200, 387017631, 186286292470278000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

K. Imatomi, M. Kaneko, E. Takeda, Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values, J. Int. Seq. 17 (2014) # 14.4.5

M. Kaneko, Poly-Bernoulli numbers

Masanobu Kaneko, Poly-Bernoulli numbers, Journal de théorie des nombres de Bordeaux, 9 no. 1 (1997), Pages 221-228.

Index entries for sequences related to Bernoulli numbers.

Formula

a(n) = denominator of Sum_{j=0..n} (-1)^(n+j) * j! * Stirling2(n, j) * (j+1)^(-k), for k = 3.

Maple

a:= (n, k)-> denom( (-1)^n*add((-1)^m*m!*Stirling2(n, m)/(m+1)^k, m=0..n)):
seq(a(n, 3), n = 0..30);

Mathematica

With[{k=3}, Table[Sum[(-1)^(n+j)*j!*StirlingS2[n, j]*(j+1)^(-k), {j, 0, n}], {n, 0, 40}]]//Denominator (* G. C. Greubel, Aug 02 2022 *)

Prog

(Magma)
A027646:= func< n, k | Denominator( (&+[(-1)^(j+n)*Factorial(j)*StirlingSecond(n, j)/(j+1)^k: j in [0..n]]) ) >;
[A027646(n, 3): n in [0..20]]; // G. C. Greubel, Aug 02 2022
(SageMath)
def A027646(n, k): return denominator( sum((-1)^(n+j)*factorial(j)*stirling_number2(n, j)/(j+1)^k for j in (0..n)) )
[A027646(n, 3) for n in (0..20)] # G. C. Greubel, Aug 02 2022

Crossrefs

Cf. A027645.

Sequence in context: A221042 A358211 A247032 * A224096 A224103 A072159

Adjacent sequences: A027643 A027644 A027645 * A027647 A027648 A027649

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved