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 A373890 #20 Jun 22 2024 14:12:03
%S A373890 1,2,11,64,345,1824,9661,51284,272333,1445995,7677250,40760798,
%T A373890 216412235,1149004281,6100444144,32389272248,171965334801,
%U A373890 913020717480,4847528344990,25737127996244,136646907481155,725503534206186,3851937726561990,20451208781128462
%N A373890 Number of compositions of 8*n into parts 1 and 8.
%H A373890 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,56,-70,56,-28,8,-1).
%F A373890 a(n) = A005710(8*n).
%F A373890 a(n) = Sum_{k=0..n} binomial(n+7*k,n-k).
%F A373890 a(n) = 9*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
%F A373890 G.f.: 1/(1 - x - x/(1 - x)^7).
%o A373890 (PARI) a(n) = sum(k=0, n, binomial(n+7*k, n-k));
%Y A373890 Cf. A052544, A055988, A369836, A371125, A373907.
%Y A373890 Cf. A005710.
%K A373890 nonn,easy
%O A373890 0,2
%A A373890 _Seiichi Manyama_, Jun 22 2024