Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture
نویسندگان
چکیده
The 2-adic valuations of Bell and complementary Bell numbers is determined. The complementary Bell numbers are known to be zero at n = 2 and H. S. Wilf conjectured that this is the only case where vanishing occurs. N. C. Alexander and J. An prove (independently) that there are at most two indices where this happens. This paper presents yet an alternative proof of the latter.
منابع مشابه
Vd 2 Draft
T. Amdeberhan, V. De Angelis, and V.H. Moll study the arithmetical properties of the complementary Bell numbers using an infinite matrix P whose basis is the falling factorials. This paper constructs a similar matrix whose basis is the rising factorials and parallels many of the same results.
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