A297210 Expansion of e.g.f. log(1 + arcsinh(x))*exp(-x).

0, 1, -3, 7, -16, 48, -213, 1027, -4856, 32512, -309377, 2527963, -16805072, 179877332, -2916171997, 32511289795, -227822369168, 3575741575680, -98643332014049, 1352701143217491, -6534261348983096, 168508582018012980, -9094443640555413357, 143341194607564099595

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2017

Keywords

• sign

Examples

			log(1 + arcsinh(x))*exp(-x) = x/1! - 3*x^2/2! + 7*x^3/3! - 16*x^4/4! + 48*x^5/5! - 213*x^6/6! + ...
		

Crossrefs

Cf. A009337, A009356, A009374, A009393, A296435, A296437, A297209, A297211, A297213.

Programs

Maple

a:=series(log(1+arcsinh(x))*exp(-x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 23; CoefficientList[Series[Log[1 + ArcSinh[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!