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A296545
Expansion of e.g.f. arcsinh(exp(x)-1).
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
0,5
LINKS
FORMULA
E.g.f.: -log(1 - exp(x) + sqrt(1 + (1 - exp(x))^2)).
EXAMPLE
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! + ...
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]!
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 15 2017
STATUS
approved