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%I #9 Dec 21 2020 17:40:07
%S 1,1,2,5,15,50,179,675,2649,10734
%N Number of permutations of length n that are sorted to the identity by a consecutive-312-avoiding-stack followed by a classical-21-avoiding stack.
%H C. Defant and K. Zheng, <a href="https://arxiv.org/abs/2008.12297">Stack-Sorting with Consecutive-Pattern-Avoiding Stacks</a>, arXiv:2008.12297 [math.CO], 2020.
%e Sending the permutation 132 through a consecutive-312-avoiding stack results in 231, and a classical 21-avoiding stack then sends 231 to 213, which is not the identity 123. Applying this procedure to any permutation of length 3 other than 132 results in 123, so a(3)=5.
%Y Cf. A033321, A001006, A337495, A011782, A001405
%K nonn,more
%O 0,3
%A _Colin Defant_, Aug 30 2020