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 A364865 #10 Aug 11 2023 09:52:03
%S A364865 1,1,3,11,43,170,657,2392,7675,17603,-11898,-529678,-4783303,
%T A364865 -33099464,-201744488,-1130700432,-5917753701,-28985131575,
%U A364865 -131668554663,-540199800203,-1862208441834,-4014999475540,10784817197302,222255824910088,1973412557775753
%N A364865 G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^4).
%F A364865 a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(4*n+k+1,n) / (4*n+k+1).
%F A364865 a(n) = (1/n) * Sum_{k=0..n-1} (-2)^k * binomial(n,k) * binomial(5*n-k,n-1-k) for n > 0.
%F A364865 a(n) = (1/n) * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * binomial(4*n,k-1) for n > 0.
%o A364865 (PARI) a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));
%Y A364865 Cf. A291534, A364864, A364866.
%Y A364865 Cf. A002294, A336540.
%K A364865 sign
%O A364865 0,3
%A A364865 _Seiichi Manyama_, Aug 11 2023