On a conjecture of Wilf

Abstract. Let n and k be natural numbers and let S(n, k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum nX j=0 (−1)j S(n, j) is nonzero for all n > 2. We prove this conjecture for all n ≡ 2 and ≡ 2944838 mod 3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the irrationality of p-adic series.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Stefan De Wannemacker, Thomas Laffey, Robert Osburn
• Keywords: JCT 2007, Natural Numbers, Stirling Numbers, Sum NX