A344393 - OEIS

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

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OFFSET

0,8

COMMENTS

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

LINKS

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

EXAMPLE

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]

MAPLE

T := (n, k) -> combinat:-eulerian1(n - k, k):

seq(print(seq(T(n, k), k=0..n/2)), n = 0..11);

CROSSREFS

Cf. A000800 (row sums).

Cf. A173018.

Sequence in context: A392273 A121301 A059056 * A127153 A178979 A228270

Adjacent sequences: A344390 A344391 A344392 * A344394 A344395 A344396

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, May 17 2021

STATUS

approved