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

Author

Andrey Zabolotskiy, Mar 22 2021

Keywords

• nonn
• more

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

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

Crossrefs

Cf. A087422, A227414, A342811.

Programs

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}]