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 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
 1, 120, 7560, 369600, 15765750, 617512896, 22813670880, 807723671040, 27686621927250, 925166131890000, 30286238493551040, 974802747606105600, 30933063577681246800, 969808565876506272000, 30090926129273230320000, 925249170367839629537280, 28225069296255264089522250 (list; graph; refs; listen; history; text; internal format)
 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) 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

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Last modified September 29 16:58 EDT 2023. Contains 365773 sequences. (Running on oeis4.)