

A098932


Numerators in the power series of a function f such that f(f(x)) = sin(x) where f(x) = Sum_{n>=1} a(n)/2^(n1)*x^(2n1)/(2n1)!.


3



1, 1, 3, 53, 1863, 92713, 3710155, 594673187, 329366540401, 104491760828591, 19610322215706989, 5244397496803513989, 7592640928150019948759, 2156328049189410651012985, 3923796638128806973444887205
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OFFSET

1,3


COMMENTS

Write f[x]=Sum[b[k]x^k/k!,{k,0,Infinity}]. Take b[0]=0 and b[1]=1. The remaining b[k] can be found by equating coefficients in f[f[x]]==Sin[x]. Only the odd terms are nonzero. The sequence given here contains the numerators of the series formed by multiplying (2j+1)!2^j by the jth odd term.


LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..100


EXAMPLE

f(x) = x  1/2*x^3/3!  3/2^2*x^5/5!  53/2^3*x^7/7!  1863/2^4*x^9/9! +...


PROG

(PARI) {a(n)=local(A, B, F); F=sin(x+O(x^(2*n+1))); A=F; for(i=0, 2*n1, B=serreverse(A); A=(A+subst(B, x, F))/2); if(n<1, 0, 2^(n1)*(2*n1)!*polcoeff(A, 2*n1, x))}
for(n=1, 30, print1(a(n), ", "))


CROSSREFS

Cf. A095883 (inverse).
Sequence in context: A216931 A012742 A012823 * A100444 A300420 A300683
Adjacent sequences: A098929 A098930 A098931 * A098933 A098934 A098935


KEYWORD

frac,sign


AUTHOR

Edward Scheinerman (ers(AT)jhu.edu), Oct 20 2004


EXTENSIONS

More terms from Paul D. Hanna, Dec 09 2004


STATUS

approved



