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 A369805 #16 Feb 02 2024 16:14:27
%S A369805 1,0,1,7,29,98,316,1043,3536,12083,41168,139750,473824,1607014,
%T A369805 5453022,18506947,62808496,213144034,723295969,2454483506,8329290739,
%U A369805 28265565587,95919580313,325504019213,1104600373788,3748469764612,12720462563684,43166996581876
%N A369805 Expansion of 1/(1 - x^2/(1-x)^7).
%C A369805 Number of compositions of 7*n-2 into parts 2 and 7.
%H A369805 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,35,-35,21,-7,1).
%F A369805 a(n) = A369813(7*n-2) for n > 0.
%F A369805 a(n) = 7*a(n-1) - 20*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F A369805 a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+5*k,n-2*k).
%o A369805 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^7))
%o A369805 (PARI) a(n) = sum(k=0, n\2, binomial(n-1+5*k, n-2*k));
%Y A369805 Cf. A099253, A369806, A369807, A369808, A369809.
%Y A369805 Cf. A369813.
%K A369805 nonn
%O A369805 0,4
%A A369805 _Seiichi Manyama_, Feb 01 2024