A371995 Triangle read by rows: T(n, k) = binomial(n - k, k) * subfactorial(k), for n >= 0 and 0 <= k <= floor(n/2).
1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 3, 1, 0, 6, 2, 1, 0, 10, 8, 1, 0, 15, 20, 9, 1, 0, 21, 40, 45, 1, 0, 28, 70, 135, 44, 1, 0, 36, 112, 315, 264, 1, 0, 45, 168, 630, 924, 265, 1, 0, 55, 240, 1134, 2464, 1855, 1, 0, 66, 330, 1890, 5544, 7420, 1854, 1, 0, 78, 440, 2970, 11088, 22260, 14832
Offset: 0
Examples
Triangle starts: [0] 1; [1] 1; [2] 1, 0; [3] 1, 0; [4] 1, 0, 1; [5] 1, 0, 3; [6] 1, 0, 6, 2; [7] 1, 0, 10, 8; [8] 1, 0, 15, 20, 9; [9] 1, 0, 21, 40, 45;
Programs
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Mathematica
T[n_, k_] := Binomial[n - k, k] * Subfactorial[k]; Table[T[n, k], {n, 0, 9}, {k, 0, n/2}] // MatrixForm