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 A385443 #14 Jun 29 2025 09:02:39
%S A385443 1,1,3,7,-55,-1215,-8645,150535,6200145,73698625,-1986309325,
%T A385443 -119693799225,-1993326710375,72724743316225,5768642653648875,
%U A385443 123556356142594375,-5685256808745889375,-559310285769833973375,-14644269999088713108125,813361265343230663434375
%N A385443 Expansion of e.g.f. (1/x) * Series_Reversion( x/(3*x + sqrt(9*x^2+1))^(1/3) ).
%H A385443 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A385443 E.g.f.: (1/x) * Series_Reversion( x * exp(-arcsinh(3*x)/3) ).
%F A385443 E.g.f.: ( (1/x) * Series_Reversion( x/(1 + 6*x)^(2/3) ) )^(1/4).
%F A385443 E.g.f. A(x) satisfies A(x) = exp( (1/3) * arcsinh(3*x*A(x)) ).
%F A385443 E.g.f. A(x) satisfies A(x) = (1 + 6*x*A(x)^4)^(1/6).
%F A385443 a(n) = 6^n * n! * binomial((4*n+1)/6,n)/(4*n+1).
%F A385443 a(n) = Sum_{k=0..n} (n+1)^(k-1) * (3*i)^(n-k) * A385343(n,k), where i is the imaginary unit.
%o A385443 (PARI) a(n) = 6^n*n!*binomial((4*n+1)/6, n)/(4*n+1);
%Y A385443 Cf. A001147, A384241, A385444.
%Y A385443 Cf. A385343.
%K A385443 sign
%O A385443 0,3
%A A385443 _Seiichi Manyama_, Jun 29 2025