%I #18 Aug 29 2022 04:42:20
%S 1,72,2916,87480,2165130,46766808,911952756,16415149608,277005649635,
%T 4432090394160,67810983030648,998670840996816,14231059484204628,
%U 197045439012064080,2660113426662865080,35113497231949819056,454280870438350784037,5772039294981398197176
%N a(n) = binomial(n + 7, 7)*9^n.
%C 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.
%H Vincenzo Librandi, <a href="/A173192/b173192.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (72,-2268,40824,-459270,3306744,-14880348,38263752,-43046721).
%F a(n) = C(n + 7, 7)*9^n.
%F From _Amiram Eldar_, Aug 29 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 16515072*log(9/8) - 19451943/10.
%F Sum_{n>=0} (-1)^n/a(n) = 63000000*log(10/9) - 13275423/2. (End)
%p A173192:=n->binomial(n+7,7)*9^n: seq(A173192(n), n=0..25); # _Wesley Ivan Hurt_, Jul 24 2017
%t Table[Binomial[n + 7, 7]*9^n, {n, 0, 20}]
%o (Magma) [Binomial(n+7, 7)*9^n: n in [0..20]]; // _Vincenzo Librandi_, Oct 13 2011
%Y Cf. A081139, A173000, A173187, A173188, A173191.
%K nonn,easy
%O 0,2
%A _Zerinvary Lajos_, Feb 12 2010