A296980 Expansion of e.g.f. arcsinh(log(1 + x)).

0, 1, -1, 1, 0, -2, -30, 446, -3248, 12412, 16020, -211356, -10756944, 284038272, -3556910448, 19122463296, 135073768320, -1286054192304, -108801241372368, 3952903127312016, -65667347037774720, 339816855220730784, 8862271481944986336

Offset

0,6

Links

Table of n, a(n) for n=0..22.

Example

arcsinh(log(1 + x)) = x^1/1! - x^2/2! + x^3/3! - 2*x^5/5! - 30*x^6/6! + ...

Maple

a:=series(arcsinh(log(1+x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 22; CoefficientList[Series[ArcSinh[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Log[Log[1 + x] + Sqrt[1 + Log[1 + x]^2]], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A001710, A001818, A003703, A003708, A009024, A009454, A009775, A104150, A296435, A296979, A296981, A296982.

Sequence in context: A217855 A285298 A134362 * A219706 A318477 A219869

Adjacent sequences: A296977 A296978 A296979 * A296981 A296982 A296983

Keyword

sign

Author

Ilya Gutkovskiy, Dec 22 2017

Status

approved