One class of Davenport-Schinzel sequences consists of  finite sequences over n symbols without immediate repetitions and without any subsequence of the type abab. We present a bijective encoding of such sequences by rooted plane trees with distinguished nonleaves and we give a combinatorial proof of the formula

B(2k-2n, k-n). B(k-1, 2n-k-1) / (k-n+1)

(here B(.,.) denotes binomial coefficient) for the number of such normalized sequences of length k. The formula was found by Gardy and Gouyou-Beauchamps by means of generating functions. We survey previous results concerning counting of DS sequences and mention several equivalent enumerative problems.