A297213 Expansion of e.g.f. log(1 + arctanh(x))*exp(-x).

0, 1, -3, 10, -40, 213, -1383, 11002, -100616, 1062625, -12508067, 164543938, -2368224032, 37311284645, -634900302775, 11658800863330, -229004281334768, 4804124787023265, -106986109080667043, 2524701174424967130, -62860054802079553016, 1648303843512405478485

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2017

Keywords

• sign

Examples

			log(1 + arctanh(x))*exp(-x) = x/1! - 3*x^2/2! + 10*x^3/3! - 40*x^4/4! + 213*x^5/5! - 1383*x^6/6! + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..432

Crossrefs

Cf. A009337, A009356, A009374, A009393, A202139, A296439, A297209, A297210, A297211.

Programs

Maple

S:= series(log(1+arctanh(x))*exp(-x),x,51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Jul 09 2018

Mathematica

nmax = 21; CoefficientList[Series[Log[1 + ArcTanh[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[Log[1 + (Log[1 + x] - Log[1 - x])/2] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!