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 A365218 #20 Aug 26 2023 18:17:21
%S A365218 1,1,5,34,265,2232,19766,181300,1706737,16392049,159959240,1581278838,
%T A365218 15800619070,159321921844,1618981274136,16562211506496,
%U A365218 170426473666497,1762771226922775,18316562635133813,191104193378725552,2001224271292820200
%N A365218 G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^6).
%C A365218 Conjecture: Is a(n)>0 correct? It is correct up to the first 10000 terms.
%H A365218 Seiichi Manyama, <a href="/A365218/b365218.txt">Table of n, a(n) for n = 0..956</a>
%F A365218 a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(6*n+k+1,n)/(6*n+k+1).
%F A365218 a(n) = Sum_{k=0..n} (-2)^(n-k) * binomial(6*n+k+1,k) * binomial(n-1,n-k)/(6*n+k+1).
%F A365218 a(n) = (1/(6*n+1)) * Sum_{k=0..n} (-1)^(n-k) * binomial(6*n+1,k) * binomial(n-1,n-k).
%o A365218 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n+1, k)*binomial(n-1, n-k))/(6*n+1);
%Y A365218 Cf. A291534, A364864, A364865, A364866.
%Y A365218 Cf. A002296.
%K A365218 nonn
%O A365218 0,3
%A A365218 _Seiichi Manyama_, Aug 26 2023