A137207 Number of exceptional sets of roots of type D_n. Also the number of unordered factorizations of the Coxeter element.

12, 87, 584, 3835, 25008, 162792, 1060048, 6910695, 45119100, 295038315, 1932260256, 12673336052, 83236707232, 547388545740, 3604063891104, 23755630474079, 156740823815940, 1035157282013085, 6842413166034600, 45265133475699795, 299671339559444160, 1985322768625822080

Offset

3,1

Links

Table of n, a(n) for n=3..24.

F. Chapoton Cluster algebras

Formula

a(n) = (2*(n-1)/(2*n-1))*binomial(3*n-3,n-1)-binomial(3*n-5,n-2)+4*binomial(3*n-3,n-3).

a(n) = (16*n^2-41*n+24)/(n*(2*n-1))*binomial(3*n-5,n-2).

Example

a(3)=12 because D3 is the same as A3.

Prog

(MuPAD)
modu_NC_D:=proc(n) begin (16*n*n-41*n+24)/n/(2*n-1)*binomial(3*n-5, n-2) end;
(Sage)
def A137207(n):
    return (16*n*n-41*n+24)*binomial(3*n-5, n-2)/n/(2*n-1)

Crossrefs

Cf. A001764 for type A, A045721 for type B.

Sequence in context: A369421 A183721 A180797 * A206765 A228500 A348415

Adjacent sequences: A137204 A137205 A137206 * A137208 A137209 A137210

Keyword

nonn

Author

F. Chapoton, Mar 05 2008

Extensions

a(22)-a(24) from Stefano Spezia, Feb 29 2024

Status

approved