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A027650 Poly-Bernoulli numbers B_n^(k) with k=-3. 6
1, 8, 46, 230, 1066, 4718, 20266, 85310, 354106, 1455278, 5938186, 24104990, 97478746, 393095438, 1581931306, 6356390270, 25511588986, 102304505198, 409992599626, 1642294397150, 6576150108826, 26325519044558, 105364834103146, 421647614381630, 1687155299822266 (list; graph; refs; listen; history; text; internal format)
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, E. Takeda, Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values, J. Int. Seq. 17 (2014) # 14.4.5.

K. 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 sequences related to Bernoulli numbers.

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)).

MAPLE

(-1)^n*sum( (-1)^'m'*'m'!*stirling2(n, 'm')/('m'+1)^k, 'm'=0..n);

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

CROSSREFS

Cf. A027649, A027651.

First differences of A016269.

Row 3 of array A099594.

Sequence in context: A258593 A134114 A071586 * A172064 A197238 A182542

Adjacent sequences:  A027647 A027648 A027649 * A027651 A027652 A027653

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 25 11:31 EDT 2021. Contains 346289 sequences. (Running on oeis4.)