Find the floor

Algebra Level 4

If the general term of a series is Tn=(n4+3n3+6n2+3n+1)n!T_n=(n^4+3n^3+6n^2+3n+1)n! and if n=130Tn=S\sum_{n=1}^{30} T_n=S then find S311036\large \lfloor \frac{S}{31*10^{36}} \rfloor

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