Non-Vanishing of Uppuluri-Carpenter Numbers
نویسنده
چکیده
The literature surrounding the Bell numbers is vast: see, for example, Comtet [1, Chapter 5]. Close cousins of the Bell numbers are the Uppuluri-Carpenter numbers (sometimes called the complementary Bell numbers); they count the excess of the number of set partitions of {1, . . . , n} into an even number of blocks over the number of partitions into an odd number of blocks. They are the integer coefficients Cn in ∑∞ n=0 Cn t n! = e 1−e . The first few Uppuluri-Carpenter numbers are [9, Sequence A000587]
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