login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012089 tan(arcsin(arctan(x)))=x+1/3!*x^3+9/5!*x^5+57/7!*x^7+5169/9!*x^9... 0

%I

%S 1,1,9,57,5169,-93807,31981689,-3857766903,1058896281825,

%T -286891166986335,108826313005021545,-47766338018402914215,

%U 25721485923005221938705,-16179153687877979599066575

%N tan(arcsin(arctan(x)))=x+1/3!*x^3+9/5!*x^5+57/7!*x^7+5169/9!*x^9...

%F a(n)=(2*n+1)!*sum(m=0..n, binomial(2*m,m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum(i=2*m+1..2*n+1, (2^i*stirling1(i,2*m+1)*binomial(2*n,i-1))/i!)). [Vladimir Kruchinin, Jun 15 2011]

%t With[{nn=30},Take[CoefficientList[Series[Tan[ArcSin[ArcTan[x]]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jun 12 2017 *)

%o (Maxima)

%o a(n):=(2*n+1)!*sum(binomial(2*m,m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum((2^i*stirling1(i,2*m+1)*binomial(2*n,i-1))/i!,i,2*m+1,2*n+1),m,0,n); [Vladimir Kruchinin, Jun 15 2011]

%K sign

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 12:03 EDT 2022. Contains 353807 sequences. (Running on oeis4.)