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

0,3

Links

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

Formula

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

Example

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! + ...

Prog

(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), ", ") )

Crossrefs

Cf. A221077, A221078, A221080.

Sequence in context: A000798 A135485 A210526 * A370165 A162287 A324227

Adjacent sequences: A221076 A221077 A221078 * A221080 A221081 A221082

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2012

Status

approved