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 A385371 #18 Jun 27 2025 04:34:55
%S A385371 1,1,3,14,93,804,8487,105720,1520313,24790800,451823403,9101380320,
%T A385371 200808312405,4816068148800,124749498365775,3470782979053440,
%U A385371 103225781141381745,3268196553960218880,109745731806193831635,3895876984699452280320
%N A385371 Expansion of e.g.f. 1/(1 - 2 * arcsinh(x))^(1/2).
%F A385371 E.g.f.: 1/(1 - 2 * log(x + sqrt(x^2 + 1)))^(1/2).
%F A385371 a(n) = Sum_{k=0..n} A001147(k) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385371 a(n) ~ sqrt(1 + exp(1)) * 2^n * n^n / ((exp(1) - 1)^(n + 1/2) * exp(n/2)). - _Vaclav Kotesovec_, Jun 27 2025
%o A385371 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*asinh(x))^(1/2)))
%Y A385371 Cf. A296675, A385372.
%Y A385371 Cf. A001147, A385310, A385343, A385367.
%K A385371 nonn
%O A385371 0,3
%A A385371 _Seiichi Manyama_, Jun 27 2025