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 A369838 #13 Mar 15 2024 17:37:48
%S A369838 1,4,15,60,245,1001,4085,16665,67985,277350,1131476,4615966,18831276,
%T A369838 76823991,313410816,1278589392,5216127688,21279691689,86812537085,
%U A369838 354160046356,1444829775128,5894321227301,24046447082350,98099780277675,400207434286276,1632684497403029
%N A369838 Number of compositions of 5*n-3 into parts 1 and 5.
%H A369838 Paolo Xausa, <a href="/A369838/b369838.txt">Table of n, a(n) for n = 1..1000</a>
%H A369838 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,10,-5,1).
%F A369838 a(n) = A003520(5*n-3).
%F A369838 a(n) = Sum_{k=0..n} binomial(n+1+4*k,n-1-k).
%F A369838 a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A369838 G.f.: x*(1-x)^2/((1-x)^5 - x).
%t A369838 LinearRecurrence[{6, -10, 10, -5, 1}, {1, 4, 15, 60, 245}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A369838 (PARI) a(n) = sum(k=0, n, binomial(n+1+4*k, n-1-k));
%Y A369838 Cf. A079675, A369836, A369837, A369839.
%Y A369838 Cf. A003520.
%K A369838 nonn
%O A369838 1,2
%A A369838 _Seiichi Manyama_, Feb 03 2024