%I #9 Jun 07 2024 05:20:05
%S 1,1,1,3,6,14,32,79,192,488,1244,3240,8497,22561,60309,162541,440598,
%T 1201377,3291426,9058464,25027797,69401101,193071153,538724060,
%U 1507288378,4227824974,11886150870,33488522111,94539554742,267383598840,757539956852,2149698586706,6109515731611
%N Number of tree interval posets of permutations of size n, considered up to isomorphism.
%C See Remark 24 in [Bouvel-Cioni-Izart].
%D Bridget E. Tenner. Interval Posets of Permutations. Order, 39(3):523-536, 2022.
%H Mathilde Bouvel, Lapo Cioni, and Benjamin Izart, <a href="https://arxiv.org/abs/2110.10000">The interval posets of permutations seen from the decomposition tree perspective</a>, arXiv:2110.10000 [math.CO], 2021-2024.
%H Bridget E. Tenner, <a href="https://arxiv.org/abs/2007.06142">Interval Posets for Permutations</a>, arXiv:2007.06142 [math.CO], 2020-2021.
%F Asymptotic behavior of a(n) is c*n^(-3/2)*r^n with c approximately 0.2597 and r approximately 2.9784. See M. Bouvel, L. Cioni, B. Izart (Remark 24).
%Y For the same posets but not considered up to isomorphism, see A054515.
%Y For interval posets that are not necessarily trees, see A373455 (for posets also considered up to isomorphism) and A348479 (otherwise).
%K nonn
%O 1,4
%A _Mathilde Bouvel_, Jun 06 2024