A376161 Number of support Tau-tilting modules for some algebras.
3, 5, 12, 33, 98, 306, 990, 3289, 11154, 38454, 134368, 474810, 1693812, 6091780, 22064130, 80410185, 294647250, 1084922190, 4012165080, 14895504030, 55496654460, 207431394300, 777601790940, 2922867908298, 11013796950228, 41596652545756, 157434454904160, 597029454416724, 2268232385053096
Offset: 0
Keywords
Links
- Paolo Xausa, Table of n, a(n) for n = 0..1000
- Anna Rodriguez Rasmussen, Exact Borel subalgebras of quasi-hereditary monomial algebras, arXiv:2504.01706 [math.RT], 2025. See p. 38.
- Qi Wang, Tau-tilting finite simply connected algebras, arXiv:1910.01937 [math.RT], 2019-2022.
Programs
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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
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Mathematica
A376161[n_] := CatalanNumber[n]*(9*n + 6)/(n + 2); Array[A376161, 30, 0] (* Paolo Xausa, Sep 14 2024 *)
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Sage
def a(n): return 3*(3*n+2)*binomial(2*n+4,n+2)/4/(2*n+1)/(2*n+3)
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)
Comments