A383644 a(n) is the number of zeros in the left half-plane of the Maclaurin polynomial of degree n for exp(z).
1, 2, 3, 4, 3, 4, 5, 6, 7, 6, 7, 8, 9, 10, 11, 10, 11, 12, 13, 14, 13, 14, 15, 16, 17, 16, 17, 18, 19, 20, 19, 20, 21, 22, 23, 24, 23, 24, 25, 26, 27, 26, 27, 28, 29, 30, 29, 30, 31, 32, 33, 32, 33, 34, 35, 36, 37, 36, 37, 38, 39, 40, 39, 40, 41, 42, 43, 42, 43, 44
Offset: 1
Keywords
Examples
a(4)= 4 because P(4,z) = 1 + z/1! + z^2/2! + z^3/3! + z^4/4! with 4 roots in the left half-plane: z1 = -1.729444231-.8889743761*i, z2 = -1.729444231+.8889743761*i, z3 = -.2705557689-2.504775904*i, z4 = -.2705557689+2.504775904*i
Programs
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Maple
A:=proc(n) local P, m, y, it: it:=0:P:=add(x^i/i!,i=0..n): y:=[fsolve(expand(P), x, complex)]: for m from 1 to nops(y) do: if Re(y[m])<0 then it:=it+1:else fi: od: A(n):=it:end proc: seq(A(n), n=1..70);
Comments