The sequence https://oeis.org/A287326 - is Binomial distributed triangular array, that shows us necessary items to expand perfect cube $n^3$. Summation of $n$-th row of Triangle A287326 from $0$ to $n-1$ returns $n^3$. But is it exist simillar patterns in order to receive expansion of power $n>3$, where $n$ - positive integer?

$$ \begin{matrix} & & & & & 1\\ & & & & 1 & & 1\\ & & & 1 & & 7& & 1\\ & & 1 & & 13& & 13& & 1\\ & 1 & & 19& & 25& & 19& & 1\\ \end{matrix} $$ Figure 1. Triangle A287326.

It derived by means of identity $$ x^3=\sum\limits_{m=0}^{x-1}3!\cdot mx-3!\cdot m^2+1 $$

For detailed info on derivation, please, reffer to links below. Thank you !

• Derivation of A287326: https://kolosovpetro.github.io/pdf/Overview_of_preprint_1603.02468.pdf
• Dedicated preprint: https://kolosovpetro.github.io/pdf/series_representation_of_power_function.pdf