A382620 a(n) = n^(2*n-4) * (n!)^2 * (n^2)! * Pochhammer(1+1/n, n-1) / ((n^2-n+1) * (n^2-n)!).

1, 24, 72576, 4528742400, 2423748096000000, 6787796602812825600000, 72775351435975459999580160000, 2410818176289650624878632291532800000, 211160088068074747246458003999015567360000000, 43450506124990177923906533235556142284800000000000000, 19145311724106592586650799558102522667408683773722624000000000

Offset: 1

Author

Wesley Ivan Hurt, Apr 01 2025

Keywords

• nonn

Comments

Product of the entries on the border of an n X n square array with elements 1..n^2 listed in increasing order by rows.

Examples

			                                                        [1   2  3  4  5]
                                        [1   2  3  4]   [6   7  8  9 10]
                              [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
                     [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
             [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
  ------------------------------------------------------------------------
    n         1        2         3            4                 5
  ------------------------------------------------------------------------
    a(n)      1        24      72576      4528742400    2423748096000000
		

Crossrefs

Cf. A382532, A382612.

Programs

Mathematica

Table[n^(2n - 4)*(n!)^2*(n^2)!*Pochhammer[1 + 1/n, n - 1]/((n^2 - n + 1)*(n^2 - n)!), {n, 12}]

Formula

a(n) ~ 2^(3/2) * Pi^(3/2) * n^(7*n - 11/2) / exp(3*n + 1/2). - Vaclav Kotesovec, Apr 01 2025