A283811 Poly-Bernoulli numbers B_n^(k) with k = -5.

1, 32, 454, 4718, 41506, 329462, 2441314, 17234438, 117437746, 779305142, 5067707074, 32440729958, 205120773586, 1284333040022, 7978977787234, 49258610238278, 302555048903026, 1850666770922102, 11281963755617794, 68586728901231398, 416015651355490066, 2518652552044759382

Offset

0,2

Comments

a(n) is also the number of acyclic orientations of the complete bipartite graph K_{5,n}. - Vincent Pilaud, Sep 16 2020

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1282

Index entries for linear recurrences with constant coefficients, signature (20,-155,580,-1044,720).

Formula

a(n) = 120*6^n - 240*5^n + 150*4^n - 30*3^n + 2^n.

From Colin Barker, Oct 14 2020: (Start)

G.f.: (1 - x)*(1 + 13*x - 18*x^2) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)).

a(n) = 20*a(n-1) - 155*a(n-2) + 580*a(n-3) - 1044*a(n-4) + 720*a(n-5) for n>4. (End)

E.g.f.: exp(2*x)*(1 - 30*exp(x) + 150*exp(2*x) - 240*exp(3*x) + 120*exp(4*x)). - Stefano Spezia, May 18 2024

Mathematica

Table[120*6^n - 240*5^n + 150*4^n - 30*3^n + 2^n , {n, 0, 20}] (* Indranil Ghosh, Mar 17 2017 *)

Prog

(PARI) a(n) = 120*6^n - 240*5^n + 150*4^n - 30*3^n + 2^n; \\ Indranil Ghosh, Mar 17 2017
(PARI) Vec((1 - x)*(1 + 13*x - 18*x^2) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Oct 14 2020
(Python) def A283811(n): return 120*6**n - 240*5**n + 150*4**n - 30*3**n + 2**n  # Indranil Ghosh, Mar 17 2017

Crossrefs

Row 5 of array A099594.

Sequence in context: A135217 A274802 A274748 * A066580 A076070 A133348

Adjacent sequences: A283808 A283809 A283810 * A283812 A283813 A283814

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 17 2017

Status

approved