cp's OEIS Frontend

A331799 Normalized volume of the Caracol flow polytope. Also equal to the number of "unified diagrams" of the Caracol graph (see Section 4.3 and Section 5 in Benedetti et al. reference).

%I A331799 #15 Feb 23 2020 14:59:36
%S A331799 1,3,32,625,18144,705894,34603008,2051893701,143000000000,
%T A331799 11464341673642,1039964049506304,105353940923859082,
%U A331799 11793014101010071552,1445828316284179687500,192713711798795989155840,27750747808814680091687085,4293818865468117678192721920
%N A331799 Normalized volume of the Caracol flow polytope. Also equal to the number of "unified diagrams" of the Caracol graph (see Section 4.3 and Section 5 in Benedetti et al. reference).
%H A331799 C. Benedetti, R. S. González D'León, C. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip, <a href="https://arxiv.org/abs/1801.07684">A combinatorial model for computing volumes of flow polytopes</a>, arXiv:1801.07684 [math.CO], 2018-2019.
%H A331799 C. Benedetti, R. S. González D'León, C. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip, <a href="https://doi.org/10.1090/tran/7743">A combinatorial model for computing volumes of flow polytopes</a>, Trans. Amer. Math. Soc., 372 (2019), 3369-3404.
%H A331799 J. Jang and J. S. Kim, <a href="https://arxiv.org/abs/1911.10703">Volumes of flow polytopes related to caracol graphs</a>, arXiv:1911.10703 [math.CO], 2019
%H A331799 M. Yip, <a href="https://arxiv.org/abs/1910.10060">A Fuss-Catalan variation of the caracol flow polytope</a>, arXiv:1910.10060 [math.CO], 2019.
%F A331799 a(n) =  A000108(n-1)*A000272(n+1).
%F A331799 a(n) = (1/n)*binomial(2*n-2,n-1)*(n+1)^(n-1).
%F A331799 a(n) = Sum_{i>=0..n-1} binomial(2*n-2,i)*A329057(n-1,i).
%e A331799 For n=3, a(3) = 32 = 2*(3+1)^2.
%p A331799 a:=proc(n)
%p A331799   return (1/n)*binomial(2*n-2,n-1)*(n+1)^(n-1);
%p A331799 end proc:
%t A331799 Array[(1/#) Binomial[2 # - 2, # - 1] (# + 1)^(# - 1) &, 17] (* _Michael De Vlieger_, Jan 28 2020 *)
%Y A331799 Cf. A000108, A000272, A134264.
%K A331799 nonn,easy
%O A331799 1,2
%A A331799 _Alejandro H. Morales_, Jan 26 2020