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 A369837 #18 Mar 15 2024 20:43:56
%S A369837 1,5,20,80,325,1326,5411,22076,90061,367411,1498887,6114853,24946129,
%T A369837 101770120,415180936,1693770328,6909898016,28189589705,115002126790,
%U A369837 469162173146,1913991948274,7808313175575,31854760257925,129954540535600,530161974821876
%N A369837 Number of compositions of 5*n-2 into parts 1 and 5.
%H A369837 Paolo Xausa, <a href="/A369837/b369837.txt">Table of n, a(n) for n = 1..1000</a>
%H A369837 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,10,-5,1).
%F A369837 a(n) = A003520(5*n-2).
%F A369837 a(n) = Sum_{k=0..n} binomial(n+2+4*k,n-1-k).
%F A369837 a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A369837 G.f.: x*(1-x)/((1-x)^5 - x).
%t A369837 LinearRecurrence[{6, -10, 10, -5, 1}, {1, 5, 20, 80, 325}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A369837 (PARI) a(n) = sum(k=0, n, binomial(n+2+4*k, n-1-k));
%Y A369837 Cf. A079675, A369836, A369838, A369839.
%Y A369837 Cf. A003520, A055990.
%K A369837 nonn
%O A369837 1,2
%A A369837 _Seiichi Manyama_, Feb 03 2024