Different values when calculating signal's energy by hand vs MATLAB
Since I don’t know rest of the given code, I’ve decided to calculate the energy other way round.
The MATLAB code for calculating the given function’s energy is given below:
syms n; % Symbol assignment for summation

Energy_1 = symsum(power((2.3704 * exp(0.287682 * n)), 2), n, -Inf, -3); % Energy for the left-hand side of the sample domain

Energy_2 = symsum(power((2.3704 * exp(-0.287682 * n)), 2), n, 3, Inf ); % Energy for the right-hand side of the sample domain

Energy = Energy_1 + Energy_2 % Overall energy


According to this code above, the resultant overall energy becomes $E = 4.5715$.
As the number of samples increases, the result gets accurate. Also, the coefficient in the exponential’s power affects the accuracy of the result too, but this is not the main case.