OFFSET
0,2
FORMULA
E.g.f.: (arctanh x)^3 or (1-x^2)^-1 * (arctanh x)^2.
a(n) is coefficient of x^(2*n+3) in (arctanh x)^3, multiplied by (2*n+3)!/6.
a(n) = (1/4)* Sum_{p=1..2*n+2} binomial(2*n+1,p-1) Sum_{m=3..2*n+3} binomial(m,3)*abs(s(2*n+3,m))*((-p)^(m-3)+(-p)^(m-3)) where s(n,m) is Stirling number of first kind . - Ammar Khatab, Aug 13 2024
EXAMPLE
(arctanh x)^3 = x^3 + x^5 + 14/15*x^7 + 818/945*x^9 + ...
MATHEMATICA
a[n_] := SeriesCoefficient[ArcTanh[x]^3, {x, 0, 2n+3}]*(2n+3)!/6;
a /@ Range[0, 12] (* Jean-François Alcover, Mar 26 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joe Keane (jgk(AT)jgk.org)
STATUS
approved