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
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
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, Jun 25 2023
STATUS
approved