cp's OEIS Frontend

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.

%I A351223 #25 Feb 27 2025 11:03:05
%S A351223 1,120,7560,369600,15765750,617512896,22813670880,807723671040,
%T A351223 27686621927250,925166131890000,30286238493551040,974802747606105600,
%U A351223 30933063577681246800,969808565876506272000,30090926129273230320000,925249170367839629537280,28225069296255264089522250
%N 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.
%F A351223 a(n) = (3*(n - 1))!/(6*((n - 2)!)^3).
%F A351223 With F the generalized hypergeometric function: (Start)
%F A351223 O.g.f.: x^2*F([4/3, 5/3, 2], [1, 1], 27*x).
%F A351223 E.g.f.: x^2*F([4/3, 5/3, 2], [1, 1, 3], 27*x)/2. (End)
%F A351223 a(n) ~ 3^(3*n-7/2)*n^2/(4*Pi). - _Stefano Spezia_, Dec 25 2024
%F A351223 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
%e A351223 a(2) = 1:
%e A351223     1
%e A351223    / \
%e A351223   2 - 3
%e A351223 with the set of the sets of the side integers S = {{1, 2}, {1, 3}, {2, 3}}.
%t A351223 Table[(3(n-1))!/(6((n-2)!)^3),{n,2,18}]
%Y A351223 Cf. A000142, A000578, A342467.
%K A351223 nonn
%O A351223 2,2
%A A351223 _Stefano Spezia_, Feb 05 2022