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 A369803 #25 Feb 14 2024 06:06:33
%S A369803 1,0,1,5,16,45,126,361,1046,3032,8771,25348,73252,211724,612009,
%T A369803 1769080,5113647,14781237,42725841,123501151,356986401,1031887518,
%U A369803 2982723523,8621714049,24921502864,72036871920,208226244217,601888555723,1739789499591,5028950081882
%N A369803 Expansion of 1/(1 - x^2/(1-x)^5).
%C A369803 Number of compositions of 5*n-2 into parts 2 and 5.
%H A369803 Seiichi Manyama, <a href="/A369803/b369803.txt">Table of n, a(n) for n = 0..1000</a>
%H A369803 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,10,-5,1).
%F A369803 a(n) = A001687(5*n-1) for n > 0.
%F A369803 a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.
%F A369803 a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+3*k,n-2*k).
%F A369803 a(n) = A369840(n)-A369840(n-1). - _R. J. Mathar_, Feb 14 2024
%o A369803 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^5))
%o A369803 (PARI) a(n) = sum(k=0, n\2, binomial(n-1+3*k, n-2*k));
%Y A369803 Cf. A079675, A368475, A369804.
%Y A369803 Cf. A369840, A369842, A369843, A369844.
%Y A369803 Cf. A001687.
%K A369803 nonn
%O A369803 0,4
%A A369803 _Seiichi Manyama_, Feb 01 2024