OFFSET
0,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: log(1 + (log(1 + x) - log(1 - x))/2)*exp(x).
a(n) ~ -(-1)^n * (n-1)! * exp((1-exp(2))/(1+exp(2))) * ((exp(2)+1)/(exp(2)-1))^n. - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
E.g.f.: A(x) = x/1! + x^2/2! + 4*x^3/3! + 53*x^5/5! - 155*x^6/6! + 2364*x^7/7! - 15288*x^8/8! + ...
MAPLE
a:=series(log(1+arctanh(x))*exp(x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + ArcTanh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 + (Log[1 + x] - Log[1 - x])/2] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + atanh(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 12 2017
STATUS
approved