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 n3n^3. Summation of nn-th row of Triangle A287326 from 00 to n−1n-1 returns n3n^3. But is it exist simillar patterns in order to receive expansion of power n>3n>3, where nn - positive integer?

11117111313111925191 \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

x3=∑m=0x−13!⋅mx−3!⋅m2+1 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 !

#NumberTheory

Note by A Former Brilliant Member
3 years, 3 months ago

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