@article {KS11a,
	title = {On Moessner{\textquoteright}s theorem},
	number = {1813/22959},
	year = {2011},
	pages = {1-8},
	institution = {Cornell University},
	address = {Ithaca, NY},
	abstract = {<p>Moessner{\textquoteright}s theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers 1n, 2n, 3n, ...  Paasche{\textquoteright}s theorem is a generalization of Moessner{\textquoteright}s; by varying the parameters of the procedure, one can obtain the sequence of factorials 1!, 2!, 3!, ... or the sequence of superfactorials 1!!, 2!!, 3!!, ...  Long{\textquoteright}s theorem generalizes Moessner{\textquoteright}s in another direction, providing a procedure to generate the sequence a1n-1, (a+d)2n-1, (a+2d)3n-1, ...  Proofs of these results in the literature are typically based on combinatorics of binomial coefficients or calculational scans. In this note we give a short and revealing algebraic proof of a general theorem that contains Moessner{\textquoteright}s, Paasche{\textquoteright}s, and Long{\textquoteright}s as special cases. We also prove a generalization that gives new Moessner-type theorems.</p>
},
	issn = {1813/22959},
	attachments = {https://haslab.uminho.pt/sites/default/files/xana/files/pascal.pdf},
	author = {Dexter Kozen and Alexandra Silva}
}