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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). 0
1, 3, 32, 625, 18144, 705894, 34603008, 2051893701, 143000000000, 11464341673642, 1039964049506304, 105353940923859082, 11793014101010071552, 1445828316284179687500, 192713711798795989155840, 27750747808814680091687085, 4293818865468117678192721920 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
C. Benedetti, R. S. González D'León, C. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip, A combinatorial model for computing volumes of flow polytopes, arXiv:1801.07684 [math.CO], 2018-2019.
C. Benedetti, R. S. González D'León, C. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip, A combinatorial model for computing volumes of flow polytopes, Trans. Amer. Math. Soc., 372 (2019), 3369-3404.
J. Jang and J. S. Kim, Volumes of flow polytopes related to caracol graphs, arXiv:1911.10703 [math.CO], 2019
M. Yip, A Fuss-Catalan variation of the caracol flow polytope, arXiv:1910.10060 [math.CO], 2019.
FORMULA
a(n) = A000108(n-1)*A000272(n+1).
a(n) = (1/n)*binomial(2*n-2,n-1)*(n+1)^(n-1).
a(n) = Sum_{i>=0..n-1} binomial(2*n-2,i)*A329057(n-1,i).
EXAMPLE
For n=3, a(3) = 32 = 2*(3+1)^2.
MAPLE
a:=proc(n)
return (1/n)*binomial(2*n-2, n-1)*(n+1)^(n-1);
end proc:
MATHEMATICA
Array[(1/#) Binomial[2 # - 2, # - 1] (# + 1)^(# - 1) &, 17] (* Michael De Vlieger, Jan 28 2020 *)
CROSSREFS
Sequence in context: A278069 A370462 A295385 * A129431 A373857 A297558
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 24 02:29 EDT 2024. Contains 374575 sequences. (Running on oeis4.)