OFFSET
0,4
COMMENTS
a(32) is negative. - Vaclav Kotesovec, Oct 25 2013
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ 8*n^(n-1)*(2*sin(Pi*n/2)-Pi*cos(Pi*n/2))/((4+Pi^2)^(3/2)*exp(n)). - Vaclav Kotesovec, Oct 25 2013
EXAMPLE
E.g.f. = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 24*x^5/5! + ...
MAPLE
seq(coeff(series(factorial(n)*exp(arctanh(arcsinh(x))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018
MATHEMATICA
CoefficientList[Series[Exp[ArcTanh[ArcSinh[x]]], {x, 0, 35}], x]* Range[0, 35]! (* Vaclav Kotesovec, Oct 25 2013 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(asinh(x))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argsinh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved