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
Seiichi Manyama, Table of n, a(n) for n = 0..1103
Index entries for linear recurrences with constant coefficients, signature (35,-511,4025,-18424,48860,-69264,40320).
FORMULA
a(n) = 5040*8^n - 15120*7^n + 16800*6^n - 8400*5^n + 1806*4^n - 126*3^n + 2^n.
From Colin Barker, Oct 14 2020: (Start)
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)
E.g.f.: exp(2*x)*(5040*exp(6*x) - 15120*exp(5*x) + 16800*exp(4*x) - 8400*exp(3*x) + 1806*exp(2*x) - 126*exp(x) + 1). - Stefano Spezia, May 18 2024
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
Seiichi Manyama, Mar 17 2017
STATUS
approved