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A173155
a(n) = binomial(n + 5, 5) * 8^n.
5
1, 48, 1344, 28672, 516096, 8257536, 121110528, 1660944384, 21592276992, 268703891456, 3224446697472, 37520834297856, 425236122042368, 4710307813392384, 51140484831117312, 545498504865251328, 5727734301085138944, 59298896293587320832, 606166495445559279616
OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=5) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly five (5) u's.
LINKS
Index entries for linear recurrences with constant coefficients, signature (48,-960,10240,-61440,196608,-262144).
FORMULA
a(n) = C(n + 5, 5)*8^n, n>=0.
G.f.: 1/(1-8*x)^6. - Vincenzo Librandi, Oct 16 2011
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 96040*log(8/7) - 38470/3.
Sum_{n>=0} (-1)^n/a(n) = 262440*log(9/8) - 30910. (End)
MATHEMATICA
Table[Binomial[n + 5, 5]*8^n, {n, 0, 20}]
PROG
(Magma) [8^n* Binomial(n+5, 5): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 11 2010
STATUS
approved