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A173192
a(n) = binomial(n + 7, 7)*9^n.
3
1, 72, 2916, 87480, 2165130, 46766808, 911952756, 16415149608, 277005649635, 4432090394160, 67810983030648, 998670840996816, 14231059484204628, 197045439012064080, 2660113426662865080, 35113497231949819056, 454280870438350784037, 5772039294981398197176
OFFSET
0,2
COMMENTS
Number of n-permutations (n>=7) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 7 u's.
LINKS
Index entries for linear recurrences with constant coefficients, signature (72,-2268,40824,-459270,3306744,-14880348,38263752,-43046721).
FORMULA
a(n) = C(n + 7, 7)*9^n.
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 16515072*log(9/8) - 19451943/10.
Sum_{n>=0} (-1)^n/a(n) = 63000000*log(10/9) - 13275423/2. (End)
MAPLE
A173192:=n->binomial(n+7, 7)*9^n: seq(A173192(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017
MATHEMATICA
Table[Binomial[n + 7, 7]*9^n, {n, 0, 20}]
PROG
(Magma) [Binomial(n+7, 7)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 12 2010
STATUS
approved