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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

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

Cf. A014307, A024429, A121868.

Sequence in context: A037504 A197237 A307242 * A089040 A331237 A184262

Adjacent sequences:  A296542 A296543 A296544 * A296546 A296547 A296548

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Dec 15 2017

STATUS

approved

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Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)