A296545 Expansion of e.g.f. arcsinh(exp(x)-1).

0, 1, 1, 0, -5, -15, 46, 735, 2185, -33390, -453479, -364155, 57806200, 681966285, -3289884779, -197798065920, -1815938249585, 33917006295885, 1155429901407646, 5691720408045315, -408736165211351795, -10271257189100959590, 23948813753053818421, 6626731340918542069425, 124356774945741129842320

Offset: 0

Author

Ilya Gutkovskiy, Dec 15 2017

Keywords

• sign

Examples

			arcsinh(exp(x)-1) = x/1! + x^2/2! - 5*x^4/4! - 15*x^5/5! + 46*x^6/6! + 735*x^7/7! + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A014307, A024429, A121868.

Programs

Maple

S:= series(arcsinh(exp(x)-1),x,41):
seq(coeff(S,x,j)*j!,j=0..40); # Robert Israel, Dec 17 2017

Mathematica

nmax = 24; CoefficientList[Series[ArcSinh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[-Log[1 - Exp[x] + Sqrt[1 + (1 - Exp[x])^2]], {x, 0, nmax}], x] Range[0, nmax]!

Formula

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