A363861 Sequence related to chains in type D noncrossing partitions.

4, 6, 64, 100, 1296, 2058, 32768, 52488, 1000000, 1610510, 35831808, 57921708, 1475789056, 2392031250, 68719476736, 111612119056, 3570467226624, 5808378560022, 204800000000000, 333597619564020, 12855002631049216, 20961814674106394, 876488338465357824, 1430511474609375000, 64509974703297150976

Offset

3,1

Comments

This is counting chains in the noncrossing partition lattices of type D_n that proceed by steps of type A2, except at most one step of type A1 at the end. This is a decomposition number in the terminology of Krattenthaler and Müller.

Links

Table of n, a(n) for n=3..27.

C. Krattenthaler and T. W. Müller, Decomposition Numbers For Finite Coxeter Groups And Generalised Non-Crossing Partitions, TAMS, vol. 362, 2010.

Formula

a(n) = (n-2)*(n-1)^(n/2-1) if n is even else a(n) = (n-1)^((n+1)/2).

Prog

(Sage) print([(n-2)*(n-1)**(n/2-1) if not n % 2 else (n-1)**((n+1)/2) for n in range(3, 28)])

Crossrefs

This is for Coxeter type D what A078707 is for Coxeter type B and A152291 is for Coxeter type A.

Sequence in context: A244388 A132929 A154668 * A189790 A053489 A012898

Adjacent sequences: A363858 A363859 A363860 * A363862 A363863 A363864

Keyword

nonn,easy

Author

F. Chapoton, Jun 25 2023

Status

approved