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A363861
Sequence related to chains in type D noncrossing partitions.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, Jun 25 2023
STATUS
approved