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 A369808 #15 Feb 02 2024 16:14:59
%S A369808 1,0,0,0,0,1,7,28,84,210,463,938,1821,3563,7385,16577,39529,96315,
%T A369808 232393,546806,1251461,2801015,6189683,13647361,30281870,67918782,
%U A369808 153939843,351309676,803438125,1834160110,4170751775,9443922772,21316094357,48041401423,108291578580
%N A369808 Expansion of 1/(1 - x^5/(1-x)^7).
%C A369808 Number of compositions of 7*n-5 into parts 5 and 7.
%H A369808 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,22,-7,1).
%F A369808 a(n) = A369816(7*n-5) for n > 0.
%F A369808 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 22*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F A369808 a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+2*k,n-5*k).
%o A369808 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^7))
%o A369808 (PARI) a(n) = sum(k=0, n\5, binomial(n-1+2*k, n-5*k));
%Y A369808 Cf. A099253, A369805, A369806, A369807, A369809.
%Y A369808 Cf. A369816.
%K A369808 nonn
%O A369808 0,7
%A A369808 _Seiichi Manyama_, Feb 01 2024