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

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 !

## closed as unclear what you're asking by Max Alekseyev, Alexey Ustinov, Neil Strickland, Mikhail Katz, Daniel LoughranFeb 20 '18 at 12:32

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• If you want your post to look less like spam and more like an inquiry, post only two links: one to your repository (and put your table of contents behind the link), and the other to some work done independently by a different researcher that you do not find on OEIS. Gerhard "We Must Keep Up Appearances" Paseman, 2018.02.19. – Gerhard Paseman Feb 19 '18 at 22:21
• Dear Gerhard, thank you for your reply, excessed links removed – Petro Kolosov Feb 20 '18 at 12:29

$$x^k = \sum_{m=0}^{x-1} ((m+1)^k - m^k) = \sum_{m=0}^{x-1} \sum_{j=0}^{k-1} {k \choose j} m^j$$
• We looking not for generalization by means of finite differences (which for sure already known), we looking for generaliation of above triangle for powers $m>3$ – Petro Kolosov Feb 20 '18 at 12:07