OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=8) of 7 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (54,-1296,18144,-163296,979776,-3919104,10077696,-15116544,10077696).
FORMULA
From Colin Barker, Jul 24 2017: (Start)
G.f.: 1 / (1 - 6*x)^9.
a(n) = (2^(-7 + n)*3^(-2 + n)*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(6 + n)*(7 + n)*(8 + n)) / 35.
(End)
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 4785948/7 - 3750000*log(6/5).
Sum_{n>=0} (-1)^n/a(n) = 39530064*log(7/6) - 213275484/35. (End)
MATHEMATICA
Table[Binomial[n + 8, 8]*6^n, {n, 0, 20}]
PROG
(Magma) [6^n* Binomial(n+8, 8): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
(PARI) Vec(1 / (1 - 6*x)^9 + O(x^30)) \\ Colin Barker, Jul 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 05 2010
STATUS
approved