MathNet 2015-part-07 — 185 problems (EN–VI) Question 76

Define a sequence $a_{i, j}$ of integers such that $a_{1, n} = n^{n}$ for $n \geq 1$ and $a_{i, j} = a_{i-1, j} + a_{i-1, j+1}$ for all $i, j \geq 1$. Find the last (decimal) digit of $a_{128,1}$.