OFFSET
0,1
COMMENTS
See Prop. A.6 in Wang's reference for the table counting Tau-tilting modules for the linear quiver modulo the relation alpha*beta = 0.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Qi Wang, Tau-tilting finite simply connected algebras, arXiv:1910.01937 [math.RT], 2019-2022.
FORMULA
a(n) = 3*(3*n+2)*binomial(2*n+4,n+2)/(4*(2*n+1)*(2*n+3)).
a(n) = A329533(n)/(n + 1).
From Peter Luschny, Sep 13 2024: (Start)
a(n) = (3*n + 2) * [x^n] ((1 - 4*x)^(3/2) + 12*x - 2)/(4*x^2).
a(n) = A016789(n)*(3/2)*(2*n)! * [x^(2*n)] hypergeom([], [3], x^2).
a(n) = CatalanNumber(n)*(9*n + 6)/(n + 2).
a(n) = -(3*n + 2)*(-4)^(n + 1)*binomial(3/2, n + 2).
a(n) = 2^n*(9*n + 6)*(2*n - 1)!! / (n + 2)!.
a(n) = A007054(n) * (3*n + 2) / 2.
a(n) = 6*A023999(n + 1)/(n + 2)!. (End)
MAPLE
a := n -> -(3*n + 2)*(-4)^(n + 1)*binomial(3/2, n + 2):
seq(a(n), n = 0..28) # Peter Luschny, Sep 13 2024
MATHEMATICA
A376161[n_] := CatalanNumber[n]*(9*n + 6)/(n + 2);
Array[A376161, 30, 0] (* Paolo Xausa, Sep 14 2024 *)
PROG
(Sage)
def a(n):
return 3*(3*n+2)*binomial(2*n+4, n+2)/4/(2*n+1)/(2*n+3)
CROSSREFS
KEYWORD
nonn
AUTHOR
F. Chapoton, Sep 13 2024
STATUS
approved