A344393 T(n, k) = Eulerian1(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.

1, 1, 1, 0, 1, 1, 1, 4, 0, 1, 11, 1, 1, 26, 11, 0, 1, 57, 66, 1, 1, 120, 302, 26, 0, 1, 247, 1191, 302, 1, 1, 502, 4293, 2416, 57, 0, 1, 1013, 14608, 15619, 1191, 1, 1, 2036, 47840, 88234, 15619, 120, 0, 1, 4083, 152637, 455192, 156190, 4293, 1

Offset: 0

Author

Peter Luschny, May 17 2021

Keywords

• nonn
• tabf

Comments

The antidiagonal representation of the first order Eulerian numbers (A173018).

Examples

			Triangle starts:
[ 0] [1]
[ 1] [1]
[ 2] [1,    0]
[ 3] [1,    1]
[ 4] [1,    4,     0]
[ 5] [1,   11,     1]
[ 6] [1,   26,    11,     0]
[ 7] [1,   57,    66,     1]
[ 8] [1,  120,   302,    26,    0]
[ 9] [1,  247,  1191,   302,    1]
[10] [1,  502,  4293,  2416,   57, 0]
[11] [1, 1013, 14608, 15619, 1191, 1]
		

Crossrefs

Cf. A000800 (row sums).

Cf. A173018.

Programs

Maple

T := (n, k) -> combinat:-eulerian1(n - k, k):
seq(print(seq(T(n, k), k=0..n/2)), n = 0..11);