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
9 months, 3 weeks ago

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