%I #9 Jul 15 2023 05:49:53

%S 4,6,64,100,1296,2058,32768,52488,1000000,1610510,35831808,57921708,

%T 1475789056,2392031250,68719476736,111612119056,3570467226624,

%U 5808378560022,204800000000000,333597619564020,12855002631049216,20961814674106394,876488338465357824,1430511474609375000,64509974703297150976

%N Sequence related to chains in type D noncrossing partitions.

%C 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.

%H C. Krattenthaler and T. W. Müller, <a href="https://doi.org/10.1090/S0002-9947-09-04981-2">Decomposition Numbers For Finite Coxeter Groups And Generalised Non-Crossing Partitions</a>, TAMS, vol. 362, 2010.

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

%o (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)])

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

%K nonn,easy

%O 3,1

%A _F. Chapoton_, Jun 25 2023