This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120054 #13 Sep 01 2022 06:32:49
%S A120054 256,1280,3840,8960,17920,32256,53760,84480,126720,183040,256256,
%T A120054 349440,465920,609280,783360,992256,1240320,1532160,1872640,2266880,
%U A120054 2720256,3238400,3827200,4492800,5241600,6080256,7015680,8055040,9205760,10475520,11872256,13404160
%N A120054 a(n) = binomial(n+3,4)*4^4.
%C A120054 Number of n permutations (n>=4) of 5 objects u, v, z, x, y with repetition allowed, containing n-4 u's. Example: if n=4 then n-4 = zero (0) u, a(1)=256, if n=5 then n-4 = one (1) u, a(2)=1280, if n=6 then n-4 = two (2) u, a(3)=3840, etc.
%H A120054 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A120054 G.f.: 256/(1-x)^5.
%F A120054 a(n) = C(n+3,4)*4^4, n>=1.
%F A120054 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A120054 Sum_{n>=1} 1/a(n) = 1/192.
%F A120054 Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/8 - 1/12. (End)
%p A120054 seq(binomial(n+3,4)*4^4, n=1..36);
%t A120054 256*Binomial[Range[30]+3,4] (* or *) LinearRecurrence[{5,-10,10,-5,1},{256,1280,3840,8960,17920},30] (* _Harvey P. Dale_, Jul 19 2018 *)
%Y A120054 Cf. A035008, A008586, A038231.
%K A120054 nonn,easy
%O A120054 1,1
%A A120054 _Zerinvary Lajos_, Aug 07 2008