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!)
 A280796 E.g.f. sqrt(1 - F(x)^2), where F(F(x)) = sin(x). 2
 1, -1, -1, -13, -367, -18549, -1465953, -166262441, -25526158559, -5088504559209, -1277203721141441, -394351281523218693, -147069662568684159055, -65255038602423680990301, -33992871584988519888865825, -20539580068386370855911967393, -14240009948449682448965044873663, -11224227759618581623496389602591953, -9984932631658989030110444663072663937, -9963529315662216629464111409263738683133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This sequence appears to consist entirely of integers. LINKS Paul D. Hanna, Table of n, a(n) for n = 0..100 FORMULA E.g.f. A(x) satisfies: A(F(x)) = cos(x), where F(F(x)) = sin(x). EXAMPLE E.g.f.: A(x) = 1 - x^2/2! - x^4/4! - 13*x^6/6! - 367*x^8/8! - 18549*x^10/10! - 1465953*x^12/12! - 166262441*x^14/14! - 25526158559*x^16/16! - 5088504559209*x^18/18! - 1277203721141441*x^20/20! - 394351281523218693*x^22/22! - 147069662568684159055*x^24/24! - 65255038602423680990301*x^26/26! +... such that A(x) = sqrt(1 - F(x)^2) where F(F(x)) = sin(x) and F(x) begins: F(x) = x - 1/2*x^3/3! - 3/4*x^5/5! - 53/8*x^7/7! - 1863/16*x^9/9! - 92713/32*x^11/11! - 3710155/64*x^13/13! + 594673187/128*x^15/15! + 329366540401/256*x^17/17! + 104491760828591/512*x^19/19! + 19610322215706989/1024*x^21/21!  - 5244397496803513989/2048*x^23/23! - 7592640928150019948759/4096*x^25/25! +... Also, e.g.f. A(x) satisfies: A(F(x)) = cos(x). PROG (PARI) {a(n)=local(A, B, F); F=sin(x+O(x^(2*n+1))); A=F; for(i=0, 2*n-1, B=serreverse(A); A=(A+subst(B, x, F))/2); (2*n)!*polcoeff(sqrt(1-A^2), 2*n, x)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A098932, A280795. Sequence in context: A165391 A061015 A330255 * A183472 A009040 A009085 Adjacent sequences:  A280793 A280794 A280795 * A280797 A280798 A280799 KEYWORD sign AUTHOR Paul D. Hanna, Jan 13 2017 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 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)