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

Author

F. Chapoton, Jun 25 2023

Keywords

• nonn
• easy

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

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

Crossrefs

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

Programs

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)])

Formula

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