The [[Forward Difference]] of some [[Sequence]] $x_n$ is the difference between the sequence at $n$ and $n-1$, denoted as $\Delta x_{n}$. $\huge \Delta x_{n} = x_{n+1} - x_{n} $ To denote the $n$-th order [[Forward Difference]] of a sequence, it is denoted as: $\huge \Delta^{n} x_{n} = \Delta \Delta^{n-1} x_{n} $ The [[Forward Difference]] relates to [[Umbral Calculus]] as can be thought of as the [[Discrete]] version of the [[Derivative]].