A344392 T(n, k) = k!*Stirling2(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.

1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 6, 0, 1, 14, 6, 0, 1, 30, 36, 0, 1, 62, 150, 24, 0, 1, 126, 540, 240, 0, 1, 254, 1806, 1560, 120, 0, 1, 510, 5796, 8400, 1800, 0, 1, 1022, 18150, 40824, 16800, 720, 0, 1, 2046, 55980, 186480, 126000, 15120

Offset: 0

Author

Peter Luschny, May 17 2021

Keywords

• nonn
• tabf

Comments

The antidiagonal representation of the Fubini numbers (A131689).

Examples

			Triangle starts:
[ 0] [1]
[ 1] [0]
[ 2] [0, 1]
[ 3] [0, 1]
[ 4] [0, 1, 2]
[ 5] [0, 1, 6]
[ 6] [0, 1, 14, 6]
[ 7] [0, 1, 30, 36]
[ 8] [0, 1, 62, 150, 24]
[ 9] [0, 1, 126, 540, 240]
[10] [0, 1, 254, 1806, 1560, 120]
[11] [0, 1, 510, 5796, 8400, 1800]
		

Crossrefs

Cf. A105795 (row sums).

Cf. A019538, A131689, A048993.

Programs

Maple

T := (n, k) -> k!*Stirling2(n - k, k):
seq(seq(T(n, k), k=0..n/2), n = 0..11);