A328001 T(n, k) = k!*(n-k)!/(floor(k/2)!*floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.
1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 6, 6, 4, 6, 6, 30, 6, 12, 12, 6, 30, 20, 30, 12, 36, 12, 30, 20, 140, 20, 60, 36, 36, 60, 20, 140, 70, 140, 40, 180, 36, 180, 40, 140, 70, 630, 70, 280, 120, 180, 180, 120, 280, 70, 630, 252, 630, 140, 840, 120, 900, 120, 840, 140, 630, 252
Offset: 0
Examples
1;
1, 1;
2, 1, 2;
6, 2, 2, 6;
6, 6, 4, 6, 6;
30, 6, 12, 12, 6, 30;
20, 30, 12, 36, 12, 30, 20;
140, 20, 60, 36, 36, 60, 20, 140;
70, 140, 40, 180, 36, 180, 40, 140, 70;
630, 70, 280, 120, 180, 180, 120, 280, 70, 630;
Programs
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Maple
T := (n, k) -> k!*(n-k)!/(iquo(k, 2)!*iquo(n-k, 2)!)^2: seq(seq(T(n,k), k=0..n), n=0..10);
Formula
T(n, k) = s(k)*s(n-k) where s(n) = A056040(n).