A284033 Poly-Bernoulli numbers B_n^(k) with k = -9.

1, 512, 38854, 1455278, 37712866, 779305142, 13821281314, 219680806598, 3216941445106, 44222780245622, 578333776748674, 7265797378375718, 88340967898764946, 1045408905465897302, 12094777018030598434, 137292855542017989638

Offset: 0

Author

Seiichi Manyama, Mar 18 2017

Keywords

• nonn

Comments

a(n) is also the number of acyclic orientations of the complete bipartite graph K_{9,n}. - Vincent Pilaud, Sep 16 2020

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..994
• Index entries for linear recurrences with constant coefficients, signature (54,-1266,16884,-140889,761166,-2655764,5753736,-6999840,3628800).

Crossrefs

Row 9 of array A099594.

Programs

Mathematica

Table[362880*10^n - 1451520*9^n + 2328480*8^n - 1905120*7^n + 834120*6^n - 186480*5^n + 18150*4^n - 510*3^n + 2^n, {n, 0, 20}] (* Indranil Ghosh, Mar 19 2017 *)
LinearRecurrence[{54,-1266,16884,-140889,761166,-2655764,5753736,-6999840,3628800},{1,512,38854,1455278,37712866,779305142,13821281314,219680806598,3216941445106},20] (* Harvey P. Dale, Dec 18 2022 *)

PARI

a(n) = 362880*10^n - 1451520*9^n + 2328480*8^n - 1905120*7^n + 834120*6^n - 186480*5^n + 18150*4^n - 510*3^n + 2^n; \\ Indranil Ghosh, Mar 19 2017

Python

def a(n): return 362880*10**n - 1451520*9**n + 2328480*8**n - 1905120*7**n + 834120*6**n - 186480*5**n + 18150*4**n - 510*3**n + 2**n # Indranil Ghosh, Mar 19 2017

Formula

a(n) = 362880*10^n - 1451520*9^n + 2328480*8^n - 1905120*7^n + 834120*6^n - 186480*5^n + 18150*4^n - 510*3^n + 2^n.