A283811 - OEIS

%I #32 Dec 30 2024 13:42:44

%S 1,32,454,4718,41506,329462,2441314,17234438,117437746,779305142,

%T 5067707074,32440729958,205120773586,1284333040022,7978977787234,

%U 49258610238278,302555048903026,1850666770922102,11281963755617794,68586728901231398,416015651355490066,2518652552044759382

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

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

%H Seiichi Manyama, <a href="/A283811/b283811.txt">Table of n, a(n) for n = 0..1282</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (20,-155,580,-1044,720).

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

%F From _Colin Barker_, Oct 14 2020: (Start)

%F 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)).

%F 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)

%F 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

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

%t LinearRecurrence[{20,-155,580,-1044,720},{1,32,454,4718,41506},30] (* _Harvey P. Dale_, Dec 30 2024 *)

%o (PARI) a(n) = 120*6^n - 240*5^n + 150*4^n - 30*3^n + 2^n; \\ _Indranil Ghosh_, Mar 17 2017

%o (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

%o (Python) def A283811(n): return 120*6**n - 240*5**n + 150*4**n - 30*3**n + 2**n  # _Indranil Ghosh_, Mar 17 2017

%Y Row 5 of array A099594.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Mar 17 2017