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 A385440 #13 Jul 04 2025 04:53:18
%S A385440 1,1,5,48,693,13440,328185,9676800,334639305,13284311040,595505854125,
%T A385440 29756856729600,1640160546688125,98860780014796800,
%U A385440 6469121228247302625,456736803668361216000,34607895888408878660625,2801319062499282124800000,241247999301688986945463125
%N A385440 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^2) ).
%F A385440 E.g.f. A(x) satisfies A(x) = (1 + 2*x*A(x)^3)^(1/2).
%F A385440 a(n) = 2^n * n! * binomial((3*n+1)/2,n)/(3*n+1).
%F A385440 a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385440 a(n) ~ 3^(3*n/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Jul 04 2025
%o A385440 (PARI) a(n) = 2^n*n!*binomial((3*n+1)/2, n)/(3*n+1);
%Y A385440 Cf. A001147, A385369, A385441, A385442.
%Y A385440 Cf. A381415, A385343.
%K A385440 nonn
%O A385440 0,3
%A A385440 _Seiichi Manyama_, Jun 29 2025