This equation is used to calculate the summation: `sum_(k=1)^nk^p = 1^p+2^p+3^p+"..."+n^p`, and so expresses the sum of the first n integers each taken to the power p.
Note: This summation is also represented by Bernoulli's Formula, also called Faulhaber's Formula, which includes as coefficients the Bernoulii Numbers.
Using the following integer polynomials generates some interesting and noteworthy sets of numbers:
p=1 generates the triangular numbers, visualized as the 2D arrangement of objects like pool balls when racked-up or the pins arranged for bowling. The numbers generated are 1,3, 6, 10, 15, 21, 28, ...
p=2 generates the square pyramid numbers, visualized as the 3-D arrangement of objects stacked to form a pyramid. The numbers generated are 1, 5, 14, 30, 55, 91, ...
p=3 generates the squared triangular numbers, visualized as 2d arrangement of objects stacked in progressively larger square matrices. The numbers generated are 1, 9, 36, 100, 225, 441, ...
p=4 generates the number: `n(n+1)(2n+1)(3n^2 + 3n -1)`/30
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