|
%I #15 Aug 29 2022 04:41:54
%S 1,48,1344,28672,516096,8257536,121110528,1660944384,21592276992,
%T 268703891456,3224446697472,37520834297856,425236122042368,
%U 4710307813392384,51140484831117312,545498504865251328,5727734301085138944,59298896293587320832,606166495445559279616
%N a(n) = binomial(n + 5, 5) * 8^n.
%C 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.
%H Vincenzo Librandi, <a href="/A173155/b173155.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (48,-960,10240,-61440,196608,-262144).
%F a(n) = C(n + 5, 5)*8^n, n>=0.
%F G.f.: 1/(1-8*x)^6. - _Vincenzo Librandi_, Oct 16 2011
%F From _Amiram Eldar_, Aug 29 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 96040*log(8/7) - 38470/3.
%F Sum_{n>=0} (-1)^n/a(n) = 262440*log(9/8) - 30910. (End)
%t Table[Binomial[n + 5, 5]*8^n, {n, 0, 20}]
%o (Magma) [8^n* Binomial(n+5, 5): n in [0..20]]; // _Vincenzo Librandi_, Oct 16 2011
%Y Cf. A081138, A140802, A175210, A140406, A053107, A141054.
%K nonn,easy
%O 0,2
%A _Zerinvary Lajos_, Feb 11 2010
|
