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%I #9 Nov 28 2025 14:58:06
%S 1,24,72576,4528742400,2423748096000000,6787796602812825600000,
%T 72775351435975459999580160000,2410818176289650624878632291532800000,
%U 211160088068074747246458003999015567360000000,43450506124990177923906533235556142284800000000000000,19145311724106592586650799558102522667408683773722624000000000
%N a(n) = n^(2*n-4) * (n!)^2 * (n^2)! * Pochhammer(1+1/n, n-1) / ((n^2-n+1) * (n^2-n)!).
%C 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.
%F a(n) ~ 2^(3/2) * Pi^(3/2) * n^(7*n - 11/2) / exp(3*n + 1/2). - _Vaclav Kotesovec_, Apr 01 2025
%e [1 2 3 4 5]
%e [1 2 3 4] [6 7 8 9 10]
%e [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e ------------------------------------------------------------------------
%e n 1 2 3 4 5
%e ------------------------------------------------------------------------
%e a(n) 1 24 72576 4528742400 2423748096000000
%t Table[n^(2n - 4)*(n!)^2*(n^2)!*Pochhammer[1 + 1/n, n - 1]/((n^2 - n + 1)*(n^2 - n)!), {n, 12}]
%Y Cf. A088020, A382532, A382612.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Apr 01 2025