OFFSET
1,1
COMMENTS
a(1) counts these values of 2n-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.
MATHEMATICA
z = 60; p[n_, x_] := Normal[Series[Sin[x], {x, 0, n}]];
t[n_] := x /. NSolve[p[n, x] == 0, x, z];
u[n_] := Select[t[n], Im[#] == 0 && # > 0 &];
v = Table[Length[u[n]], {n, 2, 30}]
(1/2) Table[Count[v, n], {n, 1, 40}]
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Clark Kimberling, Feb 13 2020
STATUS
approved