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A284032 Poly-Bernoulli numbers B_n^(k) with k = -8. 2
1, 256, 12866, 354106, 7107302, 117437746, 1701740006, 22447207906, 276054834902, 3216941445106, 35934231683846, 388027036757506, 4076344795442102, 41866470995832466, 422006961657805286, 4187561159054335906, 41007540680799210902, 397101660070601067826 (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_{8,n}. - Vincent Pilaud, Sep 16 2020

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1043

Index entries for linear recurrences with constant coefficients, signature (44,-826,8624,-54649,214676,-509004,663696,-362880).

FORMULA

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.

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

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

MATHEMATICA

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 *)

LinearRecurrence[{44, -826, 8624, -54649, 214676, -509004, 663696, -362880}, {1, 256, 12866, 354106, 7107302, 117437746, 1701740006, 22447207906}, 20] (* Harvey P. Dale, Jul 04 2021 *)

PROG

(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

(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

CROSSREFS

Row 8 of array A099594.

Sequence in context: A264496 A224967 A205652 * A205089 A239443 A240932

Adjacent sequences: A284029 A284030 A284031 * A284033 A284034 A284035

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 18 2017

STATUS

approved

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Last modified February 7 22:58 EST 2023. Contains 360132 sequences. (Running on oeis4.)