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

0,2

Links

Table of n, a(n) for n=0..18.

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*asinh(x))))

Crossrefs

Cf. A296675, A385367.

Cf. A385343, A385347, A385372.

Sequence in context: A089901 A375879 A352638 * A238302 A392187 A371020

Adjacent sequences: A385365 A385366 A385367 * A385369 A385370 A385371

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 26 2025

Status

approved