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.
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
KEYWORD
nonn,frac
AUTHOR
STATUS
approved