Problem in finding inverse Laplace

I have a problem with finding inverse laplace of function with Matlab. I obtained following transfer function :

I tried methods like

syms s t;
    num=[0 0 0 1.658e24 -1.163e14 6.076e15];
    den=[1 3.334e09 1.005e15 1.675e24 5.025e27 1.675e33];
    numsym=poly2sym(num);
    densym=poly2sym(den);
    transfer=numsym./densym;
    ilaplace(transfer,s,t)
but did not get any result. Also I tried to use partial fraction expansion and I wrote transfer function respect to poles and zeros but when I added  all the pieces I did not get the original transfer function.

syms s t;
num=[0 0 0 1.658e24 -1.163e14 6.076e15];
den=[1 3.334e09 1.005e15 1.675e24 5.025e27 1.675e33];
numsym=poly2sym(num);
densym=poly2sym(den);
transfer=numsym./densym;
[z,p,r]=residue(num,den);
transfer1=(z(1)/(s-p(1)))+(z(2)/(s-p(2)))+(z(3)/(s-p(3)))+(z(4)/(s-p(4)))+(z(5)/(s-p(5)));
transfer1=vpa(simplifyFraction((transfer1),'Expand',true),2)

 The transfer1 variable after simplification is order 4 in numerator while the original transfer function is order 2. I would be very thankful if anyone help me to find the transfer function of following expression by any method?

Answer 1

[Azzi Abdelmalek]

num=[0 0 0 1.658e24 -1.163e14 6.076e15];
den=[1 3.334e09 1.005e15 1.675e24 5.025e27 1.675e33];
numsym=poly2sym(num,'s');
densym=poly2sym(den,'s');
transfer=numsym./densym;
H=ilaplace(transfer)

[chess]

That returns 1658000000000000130023424*sum((r3^2*exp(r3*t))/(5*r3^4 + 13336000000*r3^3 + 3015000000000000*r3 which is not what I want