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

0,9

Comments

The antidiagonal representation of the Fubini numbers (A131689).

Links

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

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).

Cf. A019538, A131689, A048993.

Sequence in context: A330891 A089627 A306534 * A331787 A321686 A055925

Adjacent sequences: A344389 A344390 A344391 * A344393 A344394 A344395

Keyword

nonn,tabf

Author

Peter Luschny, May 17 2021

Status

approved