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.

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

Links

Table of n, a(n) for n=0..48.

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

Adjacent sequences: A362785 A362786 A362787 * A362789 A362790 A362791

Keyword

nonn,tabf

Author

Peter Luschny, May 04 2023

Status

approved