|
|
A283812
|
|
Poly-Bernoulli numbers B_n^(k) with k = -6.
|
|
2
|
|
|
1, 64, 1394, 20266, 237686, 2441314, 22934774, 202229266, 1701740006, 13821281314, 109214866454, 844558486066, 6419351203526, 48118995192514, 356641942834934, 2618939805811666, 19085432672558246, 138206899494338914, 995563711729120214
(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_{6,n}. - Vincent Pilaud, Sep 16 2020
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n.
G.f.: (1 - x)^2*(1 + 39*x + 38*x^2 - 120*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)).
a(n) = 27*a(n-1) - 295*a(n-2) + 1665*a(n-3) - 5104*a(n-4) + 8028*a(n-5) - 5040*a(n-6) for n>5.
(End)
|
|
MATHEMATICA
|
Table[720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n , {n, 0, 18}] (* Indranil Ghosh, Mar 17 2017 *)
|
|
PROG
|
(PARI) a(n) = 720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n; \\ Indranil Ghosh, Mar 17 2017
(PARI) Vec((1 - x)^2*(1 + 39*x + 38*x^2 - 120*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)) + O(x^20)) \\ Colin Barker, Oct 14 2020
(Python) def A283812(n): return 720*7**n - 1800*6**n + 1560*5**n - 540*4**n + 62*3**n - 2**n # Indranil Ghosh, Mar 17 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|