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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^(n-1)*x^(2n-1)/(2n-1)!. 3
1, -1, -3, -53, -1863, -92713, -3710155, 594673187, 329366540401, 104491760828591, 19610322215706989, -5244397496803513989, -7592640928150019948759, -2156328049189410651012985, 3923796638128806973444887205 (list; graph; refs; listen; history; text; internal format)
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 j-th 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*n-1, B=serreverse(A); A=(A+subst(B, x, F))/2); if(n<1, 0, 2^(n-1)*(2*n-1)!*polcoeff(A, 2*n-1, 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

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Last modified December 8 02:32 EST 2021. Contains 349590 sequences. (Running on oeis4.)