OFFSET
0,2
COMMENTS
Number of n-permutations (n>=4) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 4 u's.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (45,-810,7290,-32805,59049).
FORMULA
G.f.: 1/(1-9*x)^5. - R. J. Mathar, Dec 21 2011
a(n) = 45*a(n-1)-810*a(n-2)+7290*a(n-3)-32805*a(n-4)+59049*a(n-5). - Wesley Ivan Hurt, Apr 21 2021
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 2172 - 18432*log(9/8).
Sum_{n>=0} (-1)^n/a(n) = 36000*log(10/9) - 3792. (End)
MAPLE
MATHEMATICA
Table[Binomial[n + 4, 4]*9^n, {n, 0, 20}]
PROG
(Magma) [Binomial(n+4, 4)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
(PARI) a(n)=binomial(n+4, 4)*9^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 07 2010
STATUS
approved