A379606 S = (A-sin(A))/2 gives the area of a segment of the unit circle in terms of the arc length A (<= Pi). Expressing A in terms of S we get A = Sum_{n>=0} b^(2n+1)*c(n) where b = (12*S)^(1/3). Sequence gives numerators of c(n).

1, 1, 1, 1, 43, 1213, 151439, 33227, 16542537833, 887278009, 15233801224559, 9597171184603, 1374085664813273149, 1593410154419351, 53299328587804322691259, 1065024810026227256263721, 11374760871959174491194191, 70563256104582737796094772987, 657272463951301325116190773432261

Offset

0,5

Links

Table of n, a(n) for n=0..18.

Example

 A = b + b^3/60 + b^5/1400 + b^7/25200 + ..., where b = (12*S)^(1/3); the c(n) are 1, 1/60, 1/1400, 1/25200, 43/17248000, 1213/7207200000, ...

Mathematica

Numerator[CoefficientList[InverseSeries[Series[Surd[(6*(x - Sin[x])), 3], {x, 0, 40}]], x][[2 ;; -2 ;; 2]]] (* Amiram Eldar, Dec 27 2024 *)

Crossrefs

Cf. A379607 (denominators).

Sequence in context: A265658 A214100 A229432 * A122575 A014938 A235646

Adjacent sequences: A379603 A379604 A379605 * A379607 A379608 A379609

Keyword

nonn,frac

Author

Robert B Fowler, Dec 27 2024

Extensions

Edited by N. J. A. Sloane, Jan 14 2025

Status

approved