A385368 Expansion of e.g.f. 1/(1 - 3 * arcsinh(x)).
1, 3, 18, 159, 1872, 27567, 487152, 10043163, 236628864, 6272181243, 184725577728, 5984502588567, 211503539764224, 8097842686320423, 333891770433767424, 14750451600690993363, 695078159385543376896, 34800934548420464971635, 1844895428525714717343744
Offset: 0
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*asinh(x))))
Formula
E.g.f.: 1/(1 - 3 * log(x + sqrt(x^2 + 1))).
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A385372.
a(n) = Sum_{k=0..n} 3^k * k! * i^(n-k) * A385343(n,k), where i is the imaginary unit.
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