A385367 Expansion of e.g.f. 1/(1 - 2 * arcsinh(x)).

1, 2, 8, 46, 352, 3378, 38912, 522702, 8024064, 138586722, 2659565568, 56141737518, 1292851544064, 32253357421842, 866534937329664, 24943658876605902, 765883864848531456, 24985882009464388290, 863077992845681885184, 31469256501815056673070

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: 1/(1 - 2 * log(x + sqrt(x^2 + 1))).

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A385371.

a(n) = Sum_{k=0..n} 2^k * k! * i^(n-k) * A385343(n,k), where i is the imaginary unit.

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

Mathematica

With[{nn=20}, CoefficientList[Series[1/(1-2ArcSinh[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 14 2025 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*asinh(x))))

Crossrefs

Cf. A296675, A385368.

Cf. A007289, A385343, A385346, A385371.

Sequence in context: A074599 A007289 A099765 * A246386 A096656 A297014

Adjacent sequences: A385364 A385365 A385366 * A385368 A385369 A385370

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 26 2025

Status

approved