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A362788
Triangle read by rows, T(n, k) = RisingFactorial(n - k, k) * Stirling2(n - k, k), for n >= 0 and 0 <= k <= n//2, where '//' denotes integer division.
3
1, 0, 0, 1, 0, 2, 0, 3, 6, 0, 4, 36, 0, 5, 140, 60, 0, 6, 450, 720, 0, 7, 1302, 5250, 840, 0, 8, 3528, 30240, 16800, 0, 9, 9144, 151704, 196560, 15120, 0, 10, 22950, 695520, 1764000, 453600, 0, 11, 56210, 2994750, 13471920, 7761600, 332640
OFFSET
0,6
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 0;
[2] 0, 1;
[3] 0, 2;
[4] 0, 3, 6;
[5] 0, 4, 36;
[6] 0, 5, 140, 60;
[7] 0, 6, 450, 720;
[8] 0, 7, 1302, 5250, 840;
[9] 0, 8, 3528, 30240, 16800;
MAPLE
T := (n, k) -> pochhammer(n - k, k) * Stirling2(n - k, k):
seq(seq(T(n, k), k = 0..iquo(n, 2)), n = 0..12);
PROG
(SageMath)
def A362788(n, k):
return rising_factorial(n - k, k) * stirling_number2(n - k, k)
for n in range(10):
print([A362788(n, k) for k in range(n//2 + 1)])
CROSSREFS
Cf. A052512 (row sums), A362369, A362789.
Sequence in context: A276658 A079510 A216255 * A262256 A011120 A256930
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, May 04 2023
STATUS
approved