This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A221079 E.g.f.: Sum_{n>=0} arctanh(n*x)^n/n!. 4
 1, 1, 4, 29, 384, 8009, 222272, 8007621, 368537600, 20666061201, 1382898312192, 109329652877037, 10019611878850560, 1051350493309688025, 125329539339246256128, 16802547359327516681109, 2513955132693623215226880, 417301267683794684221354785 (list; graph; refs; listen; history; text; internal format)
 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 * A162287 A324227 A277357 Adjacent sequences:  A221076 A221077 A221078 * A221080 A221081 A221082 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 31 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)