Problem #349
Fibonacci Fusion
Let F_0=0, F_1=1, F_n=F_{n-1}+F_{n-2}\ for \ n>1
[( \sum_{i_{N-1}=1}^{i_N} [ ... [ ( \sum_{i_{1}=1}^{i_2}[ ( \sum_{i_{0}=1}^{i_1}F_{i_{0}})+F_2 ] ) + F_4 ] ... ]) +F_{2N}]
For N=10^5, find the value of the above expression modulo\ 10^9+7 for i_N=N