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

0,6

Links

Table of n, a(n) for n=0..55.

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

Adjacent sequences: A362786 A362787 A362788 * A362790 A362791 A362792

Keyword

nonn,tabf

Author

Peter Luschny, May 04 2023

Status

approved