OFFSET
0,3
COMMENTS
a(48) is negative. - Vaclav Kotesovec, Jan 26 2020
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
E.g.f.: 1/(1 - log(x + sqrt(1 + x^2))).
a(n) ~ 8*((4 - Pi^2)*sin(Pi*n/2) - 4*Pi*cos(Pi*n/2)) * n^(n-1) / ((4 + Pi^2)^2 * exp(n)). - Vaclav Kotesovec, Dec 18 2017
EXAMPLE
1/(1 - arcsinh(x)) = 1 + x/1! + 2*x^2/2! + 5*x^3/3! + 16*x^4/4! + 69*x^5/5! + ...
MAPLE
a:=series(1/(1-arcsinh(x)), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[1/(1 - ArcSinh[x]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[1/(1 - Log[x + Sqrt[1 + x^2]]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) x='x+O('x^99); Vec(serlaplace(1/(1-log(x+sqrt(1+x^2))))) \\ Altug Alkan, Dec 18 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 18 2017
STATUS
approved