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A173188
a(n) = binomial(n + 5, 5)*9^n.
5
1, 54, 1701, 40824, 826686, 14880348, 245525742, 3788111448, 55401129927, 775615818978, 10470813556203, 137072468372112, 1747673971744428, 21778706417122872, 266011342666286508, 3192136111995438096, 37707107822946112509, 439176902879019428046
OFFSET
0,2
COMMENTS
Number of n-permutations (n>=5) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly five (5) u's.
LINKS
Index entries for linear recurrences with constant coefficients, signature (54,-1215,14580,-98415,354294,-531441).
FORMULA
a(n) = C(n + 5, 5)*9^n.
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 184320*log(9/8) - 86835/4.
Sum_{n>=0} (-1)^n/a(n) = 450000*log(10/9) - 189645/4. (End)
MATHEMATICA
Table[Binomial[n + 5, 5]*9^n, {n, 0, 20}]
PROG
(Magma) [Binomial(n+5, 5)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 12 2010
STATUS
approved