login
A344392
T(n, k) = k!*Stirling2(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
0
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
0,9
COMMENTS
The antidiagonal representation of the Fubini numbers (A131689).
EXAMPLE
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]
MAPLE
T := (n, k) -> k!*Stirling2(n - k, k):
seq(seq(T(n, k), k=0..n/2), n = 0..11);
CROSSREFS
Cf. A105795 (row sums).
Sequence in context: A330891 A089627 A306534 * A331787 A321686 A055925
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, May 17 2021
STATUS
approved