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 A385442 #10 Jul 04 2025 05:00:35
%S A385442 1,1,9,168,4845,190080,9454725,570286080,40454959545,3300640358400,
%T A385442 304513870485825,31348317192192000,3562533636856719525,
%U A385442 443003419150516224000,59834227558379509360125,8722929933255903805440000,1365222778354029313094000625,228317457245013328565108736000
%N A385442 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^4) ).
%F A385442 E.g.f. A(x) satisfies A(x) = (1 + 2*x*A(x)^5)^(1/2).
%F A385442 a(n) = 2^n * n! * binomial((5*n+1)/2,n)/(5*n+1).
%F A385442 a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385442 a(n) ~ 5^(5*n/2) * n^(n-1) / (exp(n) * 3^(3*n/2 + 1)). - _Vaclav Kotesovec_, Jul 04 2025
%o A385442 (PARI) a(n) = 2^n*n!*binomial((5*n+1)/2, n)/(5*n+1);
%Y A385442 Cf. A001147, A385369, A385440, A385441.
%Y A385442 Cf. A385343.
%K A385442 nonn
%O A385442 0,3
%A A385442 _Seiichi Manyama_, Jun 29 2025