|
|
A283813
|
|
Poly-Bernoulli numbers B_n^(k) with k = -7.
|
|
2
|
|
|
1, 128, 4246, 85310, 1315666, 17234438, 202229266, 2193664790, 22447207906, 219680806598, 2076319823986, 19088476874870, 171615294959746, 1515094215592358, 13177154171845906, 113190802751806550, 962272631860465186, 8109687887324611718, 67845242760941615026
(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_{7,n}. - Vincent Pilaud, Sep 16 2020
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 5040*8^n - 15120*7^n + 16800*6^n - 8400*5^n + 1806*4^n - 126*3^n + 2^n.
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)).
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)
|
|
MATHEMATICA
|
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 *)
LinearRecurrence[{35, -511, 4025, -18424, 48860, -69264, 40320}, {1, 128, 4246, 85310, 1315666, 17234438, 202229266}, 30] (* Harvey P. Dale, Oct 29 2020 *)
|
|
PROG
|
(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
(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
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|