%I #27 Jul 04 2021 14:41:18
%S 1,256,12866,354106,7107302,117437746,1701740006,22447207906,
%T 276054834902,3216941445106,35934231683846,388027036757506,
%U 4076344795442102,41866470995832466,422006961657805286,4187561159054335906,41007540680799210902,397101660070601067826
%N Poly-Bernoulli numbers B_n^(k) with k = -8.
%C a(n) is also the number of acyclic orientations of the complete bipartite graph K_{8,n}. - _Vincent Pilaud_, Sep 16 2020
%H Seiichi Manyama, <a href="/A284032/b284032.txt">Table of n, a(n) for n = 0..1043</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (44,-826,8624,-54649,214676,-509004,663696,-362880).
%F a(n) = 40320*9^n - 141120*8^n + 191520*7^n - 126000*6^n + 40824*5^n - 5796*4^n + 254*3^n - 2^n.
%F G.f.: (12096*x^5-9336*x^4-3670*x^3+2855*x^2+214*x+1)*(x-1)^2 / ( (6*x-1) *(4*x-1) *(3*x-1) *(9*x-1) *(2*x-1) *(8*x-1) *(7*x-1) *(5*x-1) ). - _R. J. Mathar_, Mar 21 2017
%F a(n) = 44*a(n-1) - 826*a(n-2) + 8624*a(n-3) - 54649*a(n-4) + 214676*a(n-5) - 509004*a(n-6) + 663696*a(n-7) - 362880*a(n-8). - _Wesley Ivan Hurt_, Sep 16 2020
%t Table[40320*9^n - 141120*8^n + 191520*7^n - 126000*6^n + 40824*5^n - 5796*4^n + 254*3^n - 2^n, {n, 0, 20}] (* _Indranil Ghosh_, Mar 19 2017 *)
%t LinearRecurrence[{44,-826,8624,-54649,214676,-509004,663696,-362880},{1,256,12866,354106,7107302,117437746,1701740006,22447207906},20] (* _Harvey P. Dale_, Jul 04 2021 *)
%o (PARI) a(n) = 40320*9^n - 141120*8^n + 191520*7^n - 126000*6^n + 40824*5^n - 5796*4^n + 254*3^n - 2^n ; \\ _Indranil Ghosh_, Mar 19 2017
%o (Python) def a(n): return 40320*9**n - 141120*8**n + 191520*7**n - 126000*6**n + 40824*5**n - 5796*4**n + 254*3**n - 2**n # _Indranil Ghosh_, Mar 19 2017
%Y Row 8 of array A099594.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 18 2017