An = 2((n+1)!) + 4^n / 2(n!)n^2

1) determine whether it converges and if it does, find the limit of the sequence {An}

I realise that i need to find the dominant term of the sequnece and to divide by this and so on, but i have not seen an example where (n+1)! is an element of the sequence and this has thrown me. Any help would be highly appreciated!! Limits is not my forte!