cp's OEIS Frontend

A221079 E.g.f.: Sum_{n>=0} arctanh(n*x)^n/n!.

%I A221079 #11 Aug 16 2018 03:16:10
%S A221079 1,1,4,29,384,8009,222272,8007621,368537600,20666061201,1382898312192,
%T A221079 109329652877037,10019611878850560,1051350493309688025,
%U A221079 125329539339246256128,16802547359327516681109,2513955132693623215226880,417301267683794684221354785
%N A221079 E.g.f.: Sum_{n>=0} arctanh(n*x)^n/n!.
%H A221079 Vaclav Kotesovec, <a href="/A221079/b221079.txt">Table of n, a(n) for n = 0..250</a>
%F A221079 E.g.f.: Sum_{n>=0} log( sqrt((1+n*x)/(1-n*x)) )^n / n!.
%e A221079 E.g.f.: A(x) = 1 + x + 4*x^2/2! + 29*x^3/3! + 384*x^4/4! + 8009*x^5/5! + ...
%e A221079 where
%e A221079 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 A221079 (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 A221079 for(n=0,20,print1(a(n),", ") )
%o A221079 (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 A221079 for(n=0,20,print1(a(n),", ") )
%Y A221079 Cf. A221077, A221078, A221080.
%K A221079 nonn
%O A221079 0,3
%A A221079 _Paul D. Hanna_, Dec 31 2012