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 A385367 #19 Jul 14 2025 16:30:03
%S A385367 1,2,8,46,352,3378,38912,522702,8024064,138586722,2659565568,
%T A385367 56141737518,1292851544064,32253357421842,866534937329664,
%U A385367 24943658876605902,765883864848531456,24985882009464388290,863077992845681885184,31469256501815056673070
%N A385367 Expansion of e.g.f. 1/(1 - 2 * arcsinh(x)).
%F A385367 E.g.f.: 1/(1 - 2 * log(x + sqrt(x^2 + 1))).
%F A385367 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A385371.
%F A385367 a(n) = Sum_{k=0..n} 2^k * k! * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385367 a(n) ~ sqrt(Pi) * (1 + exp(1)) * 2^(n - 1/2) * n^(n + 1/2) / ((exp(1) - 1)^(n+1) * exp(n/2)). - _Vaclav Kotesovec_, Jun 27 2025
%t A385367 With[{nn=20},CoefficientList[Series[1/(1-2ArcSinh[x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 14 2025 *)
%o A385367 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*asinh(x))))
%Y A385367 Cf. A296675, A385368.
%Y A385367 Cf. A007289, A385343, A385346, A385371.
%K A385367 nonn,easy
%O A385367 0,2
%A A385367 _Seiichi Manyama_, Jun 26 2025