Frank Harary and Allen J. Schwenk have given a formula for counting the number of non-isomorphic caterpillars on n vertices with n > 3. Inspired by the formula of Frank Harary and Allen J. Schwenk, in this paper, we give a formula for counting the number of non-isomorphic caterpillars with the same degree sequence. © 2020 Charles Babbage Research Centre. All rights reserved.