A342812 Volume of the (n-1)-dimensional associahedron in the Loday realization, multiplied by (n-1)!.

1, 1, 7, 142, 5895, 417201, 45046558, 6891812712, 1417730229765, 377158121463025

Offset

1,3

Comments

Here the volume is relative to the unit cell of the lattice which is the intersection of Z^n with the hyperplane spanning the polytope.

Links

Table of n, a(n) for n=1..10.

Alexander Postnikov, Permutohedra, Associahedra, and Beyond, International Mathematics Research Notices, 2009, 1026-1106; arXiv:math/0507163 [math.CO], 2005. See Example 10.3.

Mathematica

a[n_] := With[{npr = Subsets[Span @@ Range@n, {2}]}, Sum[With[{ip = Ordering@p}, Total[-p[[Table[Min@ip[[ij]], {ij, npr}]]]]^(n - 1)] / Times @@ Differences[p], {p, Permutations@Range@n}]];
Table[a[n], {n, 8}]

Crossrefs

Cf. A087422, A227414, A342811.

Sequence in context: A051397 A322064 A179569 * A082157 A258176 A333088

Adjacent sequences: A342809 A342810 A342811 * A342813 A342814 A342815

Keyword

nonn,more

Author

Andrey Zabolotskiy, Mar 22 2021

Status

approved