OFFSET
0,5
LINKS
Robert Israel, Table of n, a(n) for n = 0..451
FORMULA
E.g.f.: log(1 + log(x + sqrt(1 + x^2))).
a(n) ~ 4*(Pi*cos(Pi*n/2) + 2*sin(Pi*n/2)) * n^(n-1) / ((4 + Pi^2) * exp(n)). - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
E.g.f.: A(x) = x/1! - x^2/2! + x^3/3! - 2*x^4/4! + 13*x^5/5! - 64*x^6/6! + ...
MAPLE
S:= series(ln(1+arcsinh(x)), x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Dec 12 2017
MATHEMATICA
nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) Vecrev(Pol(serlaplace(log(1 + asinh(x + O(x^30)))))) \\ Andrew Howroyd, Dec 12 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 12 2017
STATUS
approved