OFFSET
0,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Vaclav Kotesovec, Graph - The asymptotic ratio
FORMULA
E.g.f.: log(1 + log(x + sqrt(1 + x^2)))*exp(x).
a(n) ~ n! * 2*sqrt(2/Pi) * (Pi*c - 2*s) / (n^(3/2) * (4 + Pi^2)) * (1 + (c*(-192 + 208*Pi - 96*Pi^2 - 8*Pi^3 - 12*Pi^4 + Pi^5) - 2*s*(80 + 48*Pi - 40*Pi^2 + 24*Pi^3 + Pi^4 + 3*Pi^5)) / (4*(4 + Pi^2)^2 * (c*Pi - 2*s)*n)), where s = sin(1 - Pi*n/2) and c = cos(1 - Pi*n/2). - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
E.g.f.: A(x) = x/1! + x^2/2! + x^3/3! + 8*x^5/5! - 5*x^6/6! - 51*x^7/7! - 504*x^8/8! + ...
MAPLE
a:=series(log(1+arcsinh(x))*exp(x), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + asinh(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 12 2017
STATUS
approved