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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.
4
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
0,6
EXAMPLE
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;
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);
PROG
(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)])
CROSSREFS
Cf. A362790 (row sums), A362788, A362769.
Sequence in context: A143324 A287416 A097418 * A154752 A271868 A194354
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, May 04 2023
STATUS
approved