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 A385444 #17 Jun 29 2025 09:02:34
%S A385444 1,1,3,0,-195,-2160,21735,1290240,13253625,-758419200,-34777667925,0,
%T A385444 59136015863925,2148944878080000,-60019159896320625,
%U A385444 -8741374232887296000,-200253365886518319375,23678097149478739968000,2107410008390562322321875,0,-11628675802354427876266081875
%N A385444 Expansion of e.g.f. (1/x) * Series_Reversion( x/(4*x + sqrt(16*x^2+1))^(1/4) ).
%H A385444 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A385444 E.g.f.: (1/x) * Series_Reversion( x * exp(-arcsinh(4*x)/4) ).
%F A385444 E.g.f.: ( (1/x) * Series_Reversion( x/(1 + 8*x)^(5/8) ) )^(1/5).
%F A385444 E.g.f. A(x) satisfies A(x) = exp( (1/4) * arcsinh(4*x*A(x)) ).
%F A385444 E.g.f. A(x) satisfies A(x) = (1 + 8*x*A(x)^5)^(1/8).
%F A385444 a(n) = 8^n * n! * binomial((5*n+1)/8,n)/(5*n+1).
%F A385444 a(n) = Sum_{k=0..n} (n+1)^(k-1) * (4*i)^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385444 a(8*n+3) = 0 for n >= 0.
%o A385444 (PARI) a(n) = 8^n*n!*binomial((5*n+1)/8, n)/(5*n+1);
%Y A385444 Cf. A001147, A384241, A385443.
%Y A385444 Cf. A385343.
%K A385444 sign
%O A385444 0,3
%A A385444 _Seiichi Manyama_, Jun 29 2025