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 A332325 #24 Jan 21 2025 23:59:44
%S A332325 3,4,4,4,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,
%T A332325 4,4,4,5,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,4,4,5,4,4,5,4,4,5,4,4,4,4,5,
%U A332325 4,4,5,4,4,4,4,5,4,4,5,4,4,5,4,4,4,4,5,4
%N A332325 Number of Maclaurin polynomials p(2m,x) of cos(x) that have exactly n positive zeros.
%C A332325 Maclaurin polynomial p(2m,x) of cos(x) is 1 - x^2/2! + x^4/4! - ... + (-1)^m*x^(2m)/(2m)!.
%e A332325 a(1) counts these values of 2m: 2, 6, and 10. The single positive zeros of p(2,x), p(6,x), and p(10,x) are sqrt(2), 1.56990..., and 1.57079..., respectively.
%t A332325 z = 30; p[m_, x_] := Normal[Series[Cos[x], {x, 0, m }]];
%t A332325 t[n_] := x /. NSolve[p[n, x] == 0, x, z];
%t A332325 u[n_] := Select[t[n], Im[#] == 0 && # > 0 &];
%t A332325 v = Table[Length[u[n]], {n, 2, 100, 2}]
%t A332325 Table[Count[v, n], {n, 1, 10}]
%Y A332325 Cf. A332326, A332420, A358997.
%K A332325 nonn
%O A332325 1,1
%A A332325 _Clark Kimberling_, Feb 11 2020
%E A332325 More terms from _Jinyuan Wang_, Jan 21 2025