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 A385368 #15 Jun 27 2025 04:39:23
%S A385368 1,3,18,159,1872,27567,487152,10043163,236628864,6272181243,
%T A385368 184725577728,5984502588567,211503539764224,8097842686320423,
%U A385368 333891770433767424,14750451600690993363,695078159385543376896,34800934548420464971635,1844895428525714717343744
%N A385368 Expansion of e.g.f. 1/(1 - 3 * arcsinh(x)).
%F A385368 E.g.f.: 1/(1 - 3 * log(x + sqrt(x^2 + 1))).
%F A385368 E.g.f.: B(x)^3, where B(x) is the e.g.f. of A385372.
%F A385368 a(n) = Sum_{k=0..n} 3^k * k! * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385368 a(n) ~ sqrt(Pi) * (1 + exp(2/3)) * 2^(n + 1/2) * n^(n + 1/2) / (3 * (exp(2/3) - 1)^(n+1) * exp(2*n/3)). - _Vaclav Kotesovec_, Jun 27 2025
%o A385368 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*asinh(x))))
%Y A385368 Cf. A296675, A385367.
%Y A385368 Cf. A385343, A385347, A385372.
%K A385368 nonn,easy
%O A385368 0,2
%A A385368 _Seiichi Manyama_, Jun 26 2025