RLC bandpass filter transfer function

I've been tasked with finding the transfer function of the RLC filter shown below. I converted to the S-domain and used the voltage divider rule to find the output, and came up with:

$$H(s) = \frac{R}{Ls + \frac{1}{sC} + R}$$

I multiplied the numerator/denominator by \$sC\$ which resulted in:

$$H(s) = \frac{RsC}{CLs^2 + RsC + 1}$$

I plugged in the values of R = 220, C = 0.1 µF, and L = 100 mH, then used Octave to generate the transfer function with:

F = tf([220*.1E-6 0],[.1*.1E-6 220*.1E-6 1])

When I do the impulse or step response of the function I get a result of 0. I simulated the circuit in LTspice and approximated the impulse response with a sharp pulse and got something similar to a sinusoid. I know the simulation won't be exactly the same as the theoretical result, but it seems like my transfer function isn't correct.