A362209 Irregular triangle read by rows: T(n, k) is the number of k X k matrices using all the integers from 1 to k^2 and having trace equal to n, with 1 <= k <= A003056(n).
1, 0, 0, 4, 0, 4, 0, 8, 0, 4, 4320, 0, 4, 4320, 0, 0, 8640, 0, 0, 12960, 0, 0, 17280, 11496038400, 0, 0, 21600, 11496038400, 0, 0, 30240, 22992076800, 0, 0, 30240, 34488115200, 0, 0, 34560, 57480192000, 0, 0, 34560, 68976230400, 291948240981196800000
Offset: 1
Examples
Irregular triangle begins:
1;
0;
0, 4;
0, 4;
0, 8;
0, 4, 4320;
0, 4, 4320;
0, 0, 8640;
0, 0, 12960;
0, 0, 17280, 11496038400;
0, 0, 21600, 11496038400;
0, 0, 30240, 22992076800;
0, 0, 30240, 34488115200;
0, 0, 34560, 57480192000;
0, 0, 34560, 68976230400, 291948240981196800000;
...
T(5,2) = 8 since we have:
[1, 2] [1, 3] [4, 2] [4, 3]
[3, 4], [2, 4], [3, 1], [2, 1],
.
[2, 1] [2, 4] [3, 1] [3, 4]
[4, 3], [1, 3], [4, 2], [1, 2].