A379606 - cp's OEIS frontend

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 = (12S)^(1/3). Sequence gives numerators of c(n).

%I A379606 #25 Jan 15 2025 10:10:19
%S A379606 1,1,1,1,43,1213,151439,33227,16542537833,887278009,15233801224559,
%T A379606 9597171184603,1374085664813273149,1593410154419351,
%U A379606 53299328587804322691259,1065024810026227256263721,11374760871959174491194191,70563256104582737796094772987,657272463951301325116190773432261
%N 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).
%e A379606  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, ...
%t A379606 Numerator[CoefficientList[InverseSeries[Series[Surd[(6*(x - Sin[x])), 3], {x, 0, 40}]], x][[2 ;; -2 ;; 2]]] (* _Amiram Eldar_, Dec 27 2024 *)
%Y A379606 Cf. A379607 (denominators).
%K A379606 nonn,frac
%O A379606 0,5
%A A379606 _Robert B Fowler_, Dec 27 2024
%E A379606 Edited by _N. J. A. Sloane_, Jan 14 2025

cp's OEIS Frontend

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).

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 = (12S)^(1/3). Sequence gives numerators of c(n).