A280795 - OEIS

%I #10 Jan 14 2017 14:19:13

%S 2,-4,-4,-64,-1392,-36048,-68288,217764736,45152039424,6761531610496,

%T 479656304761728,-181164506307765760,-94510602811595547648,

%U -9099359091145965684736,15760449987522859047213056,8420566548360384773538111488,-5361092182457081839427169370112,-9833526816807364784720991628738560,595009928118250648162581567581609984

%N E.g.f. A(x) = F(x)^2, where F(F(x)) = sin(x).

%C This sequence appears to consist entirely of integers.

%H Paul D. Hanna, <a href="/A280795/b280795.txt">Table of n, a(n) for n = 1..100</a>

%e E.g.f.: A(x) = 2*x^2/2! - 4*x^4/4! - 4*x^6/6! - 64*x^8/8! - 1392*x^10/10! - 36048*x^12/12! - 68288*x^14/14! + 217764736*x^16/16! + 45152039424*x^18/18! + 6761531610496*x^20/20! +...

%e where A(x) = F(x)^2 such that F(F(x)) = sin(x) and F(x) begins:

%e 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! +...

%o (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); if(n<1, 0, (2*n)!*polcoeff(A^2, 2*n, x))}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A098932, A280796.

%K sign

%O 1,1

%A _Paul D. Hanna_, Jan 13 2017