This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A283813 #33 May 18 2024 14:54:28
%S A283813 1,128,4246,85310,1315666,17234438,202229266,2193664790,22447207906,
%T A283813 219680806598,2076319823986,19088476874870,171615294959746,
%U A283813 1515094215592358,13177154171845906,113190802751806550,962272631860465186,8109687887324611718,67845242760941615026
%N A283813 Poly-Bernoulli numbers B_n^(k) with k = -7.
%C A283813 a(n) is also the number of acyclic orientations of the complete bipartite graph K_{7,n}. - _Vincent Pilaud_, Sep 16 2020
%H A283813 Seiichi Manyama, <a href="/A283813/b283813.txt">Table of n, a(n) for n = 0..1103</a>
%H A283813 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (35,-511,4025,-18424,48860,-69264,40320).
%F A283813 a(n) = 5040*8^n - 15120*7^n + 16800*6^n - 8400*5^n + 1806*4^n - 126*3^n + 2^n.
%F A283813 From _Colin Barker_, Oct 14 2020: (Start)
%F A283813 G.f.: (1 - x)*(1 + 94*x + 371*x^2 - 1546*x^3 + 1200*x^4) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)).
%F A283813 a(n) = 35*a(n-1) - 511*a(n-2) + 4025*a(n-3) - 18424*a(n-4) + 48860*a(n-5) - 69264*a(n-6) + 40320*a(n-7) for n>6. (End)
%F A283813 E.g.f.: exp(2*x)*(5040*exp(6*x) - 15120*exp(5*x) + 16800*exp(4*x) - 8400*exp(3*x) + 1806*exp(2*x) - 126*exp(x) + 1). - _Stefano Spezia_, May 18 2024
%t A283813 Table[5040*8^n - 15120*7^n + 16800*6^n - 8400*5^n + 1806*4^n - 126*3^n + 2^n , {n, 0, 18}] (* _Indranil Ghosh_, Mar 17 2017 *)
%t A283813 LinearRecurrence[{35,-511,4025,-18424,48860,-69264,40320},{1,128,4246,85310,1315666,17234438,202229266},30] (* _Harvey P. Dale_, Oct 29 2020 *)
%o A283813 (PARI) a(n) = 5040*8^n - 15120*7^n + 16800*6^n - 8400*5^n + 1806*4^n - 126*3^n + 2^n ; \\ _Indranil Ghosh_, Mar 17 2017
%o A283813 (PARI) Vec((1 - x)*(1 + 94*x + 371*x^2 - 1546*x^3 + 1200*x^4) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)) + O(x^20)) \\ _Colin Barker_, Oct 14 2020
%o A283813 (Python) def A283813(n): return 5040*8**n - 15120*7**n + 16800*6**n - 8400*5**n + 1806*4**n - 126*3**n + 2**n # _Indranil Ghosh_, Mar 17 2017
%Y A283813 Row 7 of array A099594.
%K A283813 nonn,easy
%O A283813 0,2
%A A283813 _Seiichi Manyama_, Mar 17 2017