%I #11 Aug 16 2018 03:16:10

%S 1,1,4,29,384,8009,222272,8007621,368537600,20666061201,1382898312192,

%T 109329652877037,10019611878850560,1051350493309688025,

%U 125329539339246256128,16802547359327516681109,2513955132693623215226880,417301267683794684221354785

%N E.g.f.: Sum_{n>=0} arctanh(n*x)^n/n!.

%H Vaclav Kotesovec, <a href= "/A221079/b221079.txt" >Table of n, a(n) for n = 0..250</a>

%F E.g.f.: Sum_{n>=0} log( sqrt((1+n*x)/(1-n*x)) )^n / n!.

%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 29*x^3/3! + 384*x^4/4! + 8009*x^5/5! +...

%e where

%e A(x) = 1 + arctanh(x) + arctanh(2*x)^2/2! + arctanh(3*x)^3/3! + arctanh(4*x)^4/4! + arctanh(5*x)^5/5! +...

%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, atanh(m*X)^m/m!); n!*polcoeff(Egf, n)}

%o for(n=0,20,print1(a(n), "," ) )

%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, log(sqrt((1+m*x)/(1-m*X)))^m/m!); n!*polcoeff(Egf, n)}

%o for(n=0,20,print1(a(n), "," ) )

%Y Cf. A221077, A221078, A221080.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 31 2012