This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332420 #11 Jan 21 2025 23:55:41
%S A332420 3,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,
%T A332420 5,4,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,5,
%U A332420 4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,5,4
%N A332420 Number of Maclaurin polynomials p(2m-1,x) of sin(x) having exactly n positive zeros.
%C A332420 Maclaurin polynomial p(2m-1,x) of sin(x) is x - x^3/3! + x^5/5! - ... - (-1)^m*x^(2m-1)/(2m-1)!.
%e A332420 a(1) counts these values of 2m-1: 3, 5, and 11. The single zeros of p(3,x), p(5,x), and p(11,x) are sqrt(6), 3.078642..., and 3.141148..., respectively.
%t A332420 z = 60; p[n_, x_] := Normal[Series[Sin[x], {x, 0, n}]];
%t A332420 t[n_] := x /. NSolve[p[n, x] == 0, x, z];
%t A332420 u[n_] := Select[t[n], Im[#] == 0 && # > 0 &];
%t A332420 v = Table[Length[u[n]], {n, 2, 100, 2}]
%t A332420 Table[Count[v, n], {n, 1, 10}]
%Y A332420 Cf. A012265, A332325.
%K A332420 nonn
%O A332420 1,1
%A A332420 _Clark Kimberling_, Feb 13 2020
%E A332420 More terms from _Jinyuan Wang_, Jan 21 2025