A359648 Triangle read by rows. T(n, k) = (n!)^2 / (k! * (n - k)! * (floor(n/2)!)^2 * (floor(n/2) + 1)).
1, 1, 1, 1, 2, 1, 3, 9, 9, 3, 2, 8, 12, 8, 2, 10, 50, 100, 100, 50, 10, 5, 30, 75, 100, 75, 30, 5, 35, 245, 735, 1225, 1225, 735, 245, 35, 14, 112, 392, 784, 980, 784, 392, 112, 14, 126, 1134, 4536, 10584, 15876, 15876, 10584, 4536, 1134, 126
Offset: 0
Examples
Triangle T(n, k) starts: [0] 1; [1] 1, 1; [2] 1, 2, 1; [3] 3, 9, 9, 3; [4] 2, 8, 12, 8, 2; [5] 10, 50, 100, 100, 50, 10; [6] 5, 30, 75, 100, 75, 30, 5; [7] 35, 245, 735, 1225, 1225, 735, 245, 35; [8] 14, 112, 392, 784, 980, 784, 392, 112, 14; [9] 126, 1134, 4536, 10584, 15876, 15876, 10584, 4536, 1134, 126;
Programs
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Maple
T := proc(n, k) n!^2 / (k! * (n - k)! * iquo(n,2)!^2 * (iquo(n,2) + 1)) end: for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
Formula
T(n, k) = binomial(n, k) * A057977(n).