Geodesic
The \(p\)-adic valuation of the ASM numbers
Journal of integer sequences, Tome 14 (2011) no. 8
A classical formula of Legendre gives the $p$-adic valuation for factorials as a finite sum of values of the floor function. This expression can be used to produce a formula for the $p$-adic valuation of $n$ as a finite sum of periodic functions. An analogous result is established for the $p$-adic valuation of the ASM numbers. This sequence counts the number of alternating sign matrices.
Classification : 05A10, 11B75, 11Y55
Keywords: alternating sign matrices, valuations, recurrences, digit count 
@article{JIS_2011__14_8_a2,
     author = {Beyerstedt,  Erin and Moll,  Victor H. and Sun,  Xinyu},
     title = {The \(p\)-adic valuation of the {ASM} numbers},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {8},
     zbl = {1234.05014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a2/}
}
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Beyerstedt,  Erin; Moll,  Victor H.; Sun,  Xinyu. The \(p\)-adic valuation of the ASM numbers. Journal of integer sequences, Tome 14 (2011) no. 8. http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a2/