login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095883 Let F(x) be the function such that F(F(x)) = arcsin(x), then F(x) = Sum_{n>=0} a(n)/2^n*x^(2n+1)/(2n+1)!. 2
1, 1, 13, 501, 38617, 4945385, 944469221, 250727790173, 88106527550129, 39555449833828817, 22093952731139969213, 15041143328788464370373, 12273562321018687866908553, 11833097802606125967312406457 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears that there are no negative terms.

It also appears that, if arcsin(x) is changed to arcsinh(x) in the definition, the sequence obtained is the same except alternating in sign: 1, -1, 13, -501, ... - David W. Cantrell (DWCantrell(AT)sigmaxi.net), Jul 16 2009

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n)=T(2*n+1,1)*2^n*(2*n+1)!, T(n,m)=if n=m then 1 else 1/2(Co(n,m)-sum(i=m+1..n-1, T(n,i)*T(i,m))), Co(n,m)=T121408(n,m)=(m!*(sum(k=0..n-m, (-1)^((k)/2)*(sum(i=0..k, (2^i*stirling1(m+i,m)* binomial(m+k-1,m+i-1))/(m+i)!))*binomial((n-2)/2,(n-m-k)/2)))*((-1)^(n-m)+1))/2. - Vladimir Kruchinin, Nov 11 2011

EXAMPLE

F(x) = x + (1/2)*x^3/3! + (13/2^2)*x^5/5! + (501/2^3)*x^7/7! + (38617/2^4)*x^9/9! + ...

Special values:

F(x)=Pi/6 at x=F(1/2) = 0.51137532057552418592144885355...

F(x)=Pi/4 at x=F(sqrt(2)/2) = 0.74287348600976...

PROG

(PARI) {a(n)=local(A, B, F); F=asin(x+x*O(x^(2*n+1))); A=F; for(i=0, n, B=serreverse(A); A=(A+subst(B, x, F))/2); 2^n*(2*n+1)!*polcoeff(A, 2 *n+1, x)}

CROSSREFS

Cf. A095882, A095884, A095885.

Sequence in context: A281181 A183479 A203586 * A139168 A174564 A300525

Adjacent sequences:  A095880 A095881 A095882 * A095884 A095885 A095886

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 10 2004

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 18:47 EDT 2020. Contains 333323 sequences. (Running on oeis4.)