cp's OEIS Frontend

A173000 a(n) = binomial(n + 4, 4)*9^n.

%I A173000 #27 Aug 28 2022 08:29:22
%S A173000 1,45,1215,25515,459270,7440174,111602610,1578379770,21308126895,
%T A173000 277005649635,3490271185401,42835146366285,514021756395420,
%U A173000 6049640671423020,70002984912180660,798034027998859524,8977882814987169645,99812932472504415465,1097942257197548570115
%N A173000 a(n) = binomial(n + 4, 4)*9^n.
%C A173000 Number of n-permutations (n>=4) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 4 u's.
%H A173000 Vincenzo Librandi, <a href="/A173000/b173000.txt">Table of n, a(n) for n = 0..400</a>
%H A173000 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (45,-810,7290,-32805,59049).
%F A173000 G.f.: 1/(1-9*x)^5. - _R. J. Mathar_, Dec 21 2011
%F A173000 a(n) = 45*a(n-1)-810*a(n-2)+7290*a(n-3)-32805*a(n-4)+59049*a(n-5). - _Wesley Ivan Hurt_, Apr 21 2021
%F A173000 From _Amiram Eldar_, Aug 28 2022: (Start)
%F A173000 Sum_{n>=0} 1/a(n) = 2172 - 18432*log(9/8).
%F A173000 Sum_{n>=0} (-1)^n/a(n) = 36000*log(10/9) - 3792. (End)
%F A173000 a(n) = A000332(n+4)*A001019(n). - _Michel Marcus_, Aug 28 2022
%p A173000 A173000:=n->binomial(n+4,4)*9^n: seq(A173000(n), n=0..25); # _Wesley Ivan Hurt_, Jul 24 2017
%t A173000 Table[Binomial[n + 4, 4]*9^n, {n, 0, 20}]
%o A173000 (Magma) [Binomial(n+4, 4)*9^n: n in [0..20]]; // _Vincenzo Librandi_, Oct 13 2011
%o A173000 (PARI) a(n)=binomial(n+4,4)*9^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A173000 Cf. A000332, A001019.
%K A173000 nonn,easy
%O A173000 0,2
%A A173000 _Zerinvary Lajos_, Feb 07 2010