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 A367234 #19 Dec 01 2024 10:04:47
%S A367234 1,1,6,35,226,1561,11276,84150,643730,5021038,39781858,319282210,
%T A367234 2590312872,21208628405,175024439504,1454329099044,12157356271998,
%U A367234 102170610282040,862721635191860,7315768816166027,62274763166575410,531950072655682896,4558282056420235664
%N A367234 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^4.
%H A367234 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A367234 If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).
%F A367234 From _Seiichi Manyama_, Dec 01 2024: (Start)
%F A367234 G.f.: exp( Sum_{k>=1} A378567(k) * x^k/k ).
%F A367234 a(n) = (1/(n+1)) * [x^n] 1/(1 - x/(1 - x)^4)^(n+1).
%F A367234 G.f.: (1/x) * Series_Reversion( x*(1 - x/(1 - x)^4) ). (End)
%o A367234 (PARI) a(n, s=4, t=2, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
%Y A367234 Cf. A321798, A365114, A367235.
%Y A367234 Cf. A001003, A011270, A365150.
%Y A367234 Cf. A361306, A378567.
%K A367234 nonn
%O A367234 0,3
%A A367234 _Seiichi Manyama_, Nov 11 2023