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A382612 a(n) = n^3 * (n^2 - n + 1).

%I A382612 #9 Apr 15 2025 23:37:44
%S A382612 0,1,24,189,832,2625,6696,14749,29184,53217,91000,147741,229824,
%T A382612 344929,502152,712125,987136,1341249,1790424,2352637,3048000,3898881,
%U A382612 4930024,6168669,7644672,9390625,11441976,13837149,16617664,19828257,23517000,27735421,32538624,37985409,44138392,51064125,58833216,67520449,77204904,87970077,99904000,113099361,127653624
%N A382612 a(n) = n^3 * (n^2 - n + 1).
%C A382612 Product of the entries in the corners of an n X n square array with elements 1..n^2 listed in increasing order by rows (see example).
%H A382612 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A382612 G.f.: x*(1+18*x+60*x^2+38*x^3+3*x^4)/(x-1)^6. - _R. J. Mathar_, Apr 02 2025
%F A382612 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Wesley Ivan Hurt_, Apr 15 2025
%e A382612                                                         [1   2  3  4  5]
%e A382612                                         [1   2  3  4]   [6   7  8  9 10]
%e A382612                               [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
%e A382612                      [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
%e A382612              [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
%e A382612   ------------------------------------------------------------------------
%e A382612     n         1        2         3            4                 5
%e A382612   ------------------------------------------------------------------------
%e A382612               1     1*2*3*4   1*3*7*9     1*4*13*16         1*5*21*25
%e A382612   ------------------------------------------------------------------------
%e A382612     a(n)      1       24        189          832               2625
%t A382612 Table[n^3 (n^2 - n + 1), {n, 0, 60}]
%o A382612 (Magma) [n^3*(n^2 - n + 1) : n in [0..50]]; // _Wesley Ivan Hurt_, Apr 15 2025
%Y A382612 Cf. A088020 (product of all entries).
%Y A382612 Cf. A382532 (product along main antidiagonal).
%Y A382612 Cf. A382620 (product along border).
%K A382612 easy,nonn
%O A382612 0,3
%A A382612 _Wesley Ivan Hurt_, Mar 31 2025