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Number of isomorphism classes of indecomposable Fano Bott manifolds of complex dimension n.
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%I #22 Jul 05 2021 15:02:19

%S 1,1,3,7,21,60,189,595,1948,6455,21804,74464,257311,896874,3151564,

%T 11148982,39680010,141969156,510352307,1842370850,6676349598,

%U 24277171876,88556616799,323959047186,1188237214539,4368874535437,16099389598907,59449932709972,219953954227839

%N Number of isomorphism classes of indecomposable Fano Bott manifolds of complex dimension n.

%C a(n) is also the number of rooted triangular cacti with 2n+1 nodes (n triangles) with one triangle at the root vertex.

%H Yunhyung Cho, Eunjeong Lee, Mikiya Masuda, and Seonjeong Park, <a href="http://arxiv.org/abs/2106.12788">On the enumeration of Fano Bott manifolds</a>, arXiv:2106.12788 [math.AG], 2021. See Table 1 p. 8.

%H Frank Harary and George E. Uhlenbeck, <a href="https://doi.org/10.1073/pnas.39.4.315 ">On the number of Husimi trees. I</a>, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 315-322.

%F G.f.: (x/2)*(F(x^2)+F(x)^2) where F(x) is the g.f. of A003080 (see the equation (1) in [Harary-Uhlenbeck] or [Cho-Lee-Masuda-Park, Lemma 4.3]).

%Y Cf. A003080.

%K nonn

%O 1,3

%A _Eunjeong Lee_, Jun 29 2021