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

2,2

Links

Table of n, a(n) for 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

Example

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

Mathematica

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

Crossrefs

Cf. A000142, A000578, A342467.

Sequence in context: A001785 A270848 A223960 * A156411 A076005 A218503

Adjacent sequences: A351220 A351221 A351222 * A351224 A351225 A351226

Keyword

nonn

Author

Stefano Spezia, Feb 05 2022

Status

approved