A296982 Expansion of e.g.f. arctanh(log(1 + x)).

0, 1, -1, 4, -18, 118, -930, 8888, -98504, 1248784, -17790480, 281590032, -4901447232, 93064850448, -1914144990576, 42396742460928, -1006101059149440, 25466710774651776, -684902462140798848, 19503187752732408576, -586221766070655432960

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Example

arctanh(log(1 + x)) = x^1/1! - x^2/2! + 4*x^3/3! - 18*x^4/4! + 118*x^5/5! - 930*x^6/6! + ...

Maple

a:=series(arctanh(log(1+x)), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 20; CoefficientList[Series[ArcTanh[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Log[1 + Log[1 + x]]/2 - Log[1 - Log[1 + x]]/2, {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A001710, A003703, A003708, A009024, A009454, A009775, A010050, A104150, A202139, A296979, A296980, A296981.

Sequence in context: A223008 A162224 A321704 * A222375 A053529 A005442

Adjacent sequences: A296979 A296980 A296981 * A296983 A296984 A296985

Keyword

sign

Author

Ilya Gutkovskiy, Dec 22 2017

Status

approved