The 2-adic Valuation of Stirling Numbers of the Second Kind
نویسندگان
چکیده
In this paper, we investigate the 2-adic valuation of the Stirling numbers S(n, k) of the second kind. We show that v2(S(2n + 1, k + 1)) = s2(n) − 1 for any positive integer n, where s2(n) is the sum of binary digits of n. This confirms a conjecture of Amdeberhan, Manna and Moll. We show also that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i 6≡ 7 (mod 32). This proves another conjecture of Amdeberhan, Manna and Moll.
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