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A137207 Number of exceptional sets of roots of type D_n. Also the number of unordered factorizations of the Coxeter element. 1
12, 87, 584, 3835, 25008, 162792, 1060048, 6910695, 45119100, 295038315, 1932260256, 12673336052, 83236707232, 547388545740, 3604063891104, 23755630474079, 156740823815940, 1035157282013085, 6842413166034600 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..21.

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: A046023 A183721 A180797 * A206765 A228500 A082814

Adjacent sequences:  A137204 A137205 A137206 * A137208 A137209 A137210

KEYWORD

nonn

AUTHOR

F. Chapoton, Mar 05 2008

STATUS

approved

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Last modified June 14 04:54 EDT 2021. Contains 345018 sequences. (Running on oeis4.)