A362789 Triangle read by rows. T(n, k) = FallingFactorial(n - k, k) * Stirling2(n - k, k), for n >= 0 and 0 <= k <= n//2, where '//' denotes integer division.
1, 0, 0, 1, 0, 2, 0, 3, 2, 0, 4, 18, 0, 5, 84, 6, 0, 6, 300, 144, 0, 7, 930, 1500, 24, 0, 8, 2646, 10800, 1200, 0, 9, 7112, 63210, 23400, 120, 0, 10, 18360, 324576, 294000, 10800, 0, 11, 45990, 1524600, 2857680, 352800, 720, 0, 12, 112530, 6717600, 23496480, 7056000, 105840
Offset: 0
Examples
Triangle T(n, k) starts: [0] 1; [1] 0; [2] 0, 1; [3] 0, 2; [4] 0, 3, 2; [5] 0, 4, 18; [6] 0, 5, 84, 6; [7] 0, 6, 300, 144; [8] 0, 7, 930, 1500, 24; [9] 0, 8, 2646, 10800, 1200;
Programs
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Maple
fallingFactorial := (x, n) -> (-1)^n * pochhammer(-x, n): T := (n, k) -> fallingFactorial(n - k, k) * Stirling2(n - k, k): seq(seq(T(n, k), k = 0..iquo(n,2)), n = 0..12);
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SageMath
def A362789(n, k): return falling_factorial(n - k, k) * stirling_number2(n - k, k) for n in range(10): print([A362789(n, k) for k in range(n//2 + 1)])