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

1, 1, 4, 29, 384, 8009, 222272, 8007621, 368537600, 20666061201, 1382898312192, 109329652877037, 10019611878850560, 1051350493309688025, 125329539339246256128, 16802547359327516681109, 2513955132693623215226880, 417301267683794684221354785

Offset: 0

Author

Paul D. Hanna, Dec 31 2012

Keywords

• nonn

Examples

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A221077, A221078, A221080.

Programs

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)}
for(n=0,20,print1(a(n),", ") )

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)}
for(n=0,20,print1(a(n),", ") )

Formula

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