A351223 a(n) is the number of triangular arrays containing the first 3*(n - 1) positive integers arranged with number n on each side and having different set of the sets of the side integers.

1, 120, 7560, 369600, 15765750, 617512896, 22813670880, 807723671040, 27686621927250, 925166131890000, 30286238493551040, 974802747606105600, 30933063577681246800, 969808565876506272000, 30090926129273230320000, 925249170367839629537280, 28225069296255264089522250

Offset: 2

Author

Stefano Spezia, Feb 05 2022

Keywords

• nonn

Examples

			a(2) = 1:
    1
   / \
  2 - 3
with the set of the sets of the side integers S = {{1, 2}, {1, 3}, {2, 3}}.
		

Crossrefs

Cf. A000142, A000578, A342467.

Programs

Mathematica

Table[(3(n-1))!/(6((n-2)!)^3),{n,2,18}]

Formula

a(n) = (3*(n - 1))!/(6*((n - 2)!)^3).

With F the generalized hypergeometric function: (Start)

O.g.f.: x^2*F([4/3, 5/3, 2], [1, 1], 27*x).

E.g.f.: x^2*F([4/3, 5/3, 2], [1, 1, 3], 27*x)/2. (End)

a(n) ~ 3^(3*n-7/2)*n^2/(4*Pi). - Stefano Spezia, Dec 25 2024

D-finite with recurrence (n-2)^3*a(n) -3*(3*n-5)*(n-1)*(3*n-4)*a(n-1)=0. - R. J. Mathar, Feb 27 2025