The rows of Pascal's triangle are examples for logarithmically concave sequences.
In mathematics, a sequence a = (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if ai2 ≥ ai−1ai+1 holds for 0 < i < n.
Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences:
a is non-negative
a has no internal zeros; in other words, the support of a is an interval of Z.
Sequences that fulfill the three conditions are also called Pólya Frequency sequences of order 2 (PF2 sequences). Refer to chapter 2 of [1] for a discussion on the two notions. For instance, the sequence (1,1,0,0,1) satisfies the concavity inequalities but not the internal zeros condition.
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