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A296981

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

0, 1, -1, 0, 6, -22, -30, 952, -5656, -9952, 508320, -3874992, -20690208, 833780400, -7697940432, -52230156288, 2467649024640, -24686997151104, -329724479772288, 14493628861307136, -159114034671287040, -2682505451050592256, 126421889770129637376

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OFFSET

0,5

LINKS

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

FORMULA

a(n) ~ (-1)^(n+1) * (n-1)! * sin(n*(Pi-1)/2) / (2 - 2*cos(1))^(n/2). - Vaclav Kotesovec, Mar 26 2019

EXAMPLE

arctan(log(1 + x)) = x^1/1! - x^2/2! + 6*x^4/4! - 22*x^5/5! - 30*x^6/6! + ...

MAPLE

a:=series(arctan(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[ArcTan[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 22; CoefficientList[Series[(I/2) Log[1 - I Log[1 + x]] - (I/2) Log[1 + I Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A001710, A003703, A003708, A009024, A009454, A009775, A010050, A104150, A110708, A296979, A296980, A296982.

Sequence in context: A055709 A276795 A037204 * A387389 A035285 A069824

Adjacent sequences: A296978 A296979 A296980 * A296982 A296983 A296984

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Dec 22 2017

STATUS

approved

URL: https://oeis.org/A296981

⇱ A296981 - OEIS