Moessner's process for generating powers by addition is equivalent to a nested summation with index-dependent upper bounds, and this form generalizes to factorials, binomials, Catalan and polygonal numbers.
Burge (1975): Recursive Programming Techniques
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Summa Summarum: Moessner's Theorem without Dynamic Programming
Moessner's process for generating powers by addition is equivalent to a nested summation with index-dependent upper bounds, and this form generalizes to factorials, binomials, Catalan and polygonal numbers.