Could the sequence A287326 be generalized in order to receive expansion of natural power n>3?

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 !

Note by Kolosov Petro
7 months, 1 week ago

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