OFFSET
0,2
COMMENTS
a(n) is also the number of acyclic orientations of the complete bipartite graph K_{3,n}. - Vincent Pilaud, Sep 15 2020
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
K. Imatomi, M. Kaneko, and E. Takeda, Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values, J. Int. Seq. 17 (2014) # 14.4.5.
Ken Kamano, Sums of Products of Bernoulli Numbers, Including Poly-Bernoulli Numbers, J. Int. Seq. 13 (2010), 10.5.2.
Ken Kamano, Sums of Products of Poly-Bernoulli Numbers of Negative Index, Journal of Integer Sequences, Vol. 15 (2012), #12.1.3.
Masanobu Kaneko, Poly-Bernoulli numbers, Journal de théorie des nombres de Bordeaux, 9 no. 1 (1997), Pages 221-228.
Takao Komatsu, Some recurrence relations of poly-Cauchy numbers, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.
Index entries for linear recurrences with constant coefficients, signature (9,-26,24).
FORMULA
a(n) = 6*4^n - 6*3^n + 2^n. - Vladeta Jovovic, Nov 14 2003
G.f.: (1-x)/((1-2*x)*(1-3*x)*(1-4*x)).
E.g.f.: exp(2*x) - 6*exp(3*x) + 6*exp(4*x). - G. C. Greubel, Aug 02 2022
MAPLE
a:= (n, k) -> (-1)^n*sum((-1)^j*j!*Stirling2(n, j)/(j+1)^k, j=0..n);
seq(a(n, -3), n = 0..30);
MATHEMATICA
Table[6*4^n-6*3^n+2^n, {n, 0, 30}] (* G. C. Greubel, Feb 07 2018 *)
PROG
(Magma) [6*4^n-6*3^n+2^n: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011
(PARI) Vec((1-x)/((1-2*x)*(1-3*x)*(1-4*x)) + O(x^30)) \\ Michel Marcus, Feb 13 2015
(SageMath) [2^n -6*3^n +6*4^n for n in (0..30)] # G. C. Greubel, Aug 02 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved