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

%I A344393 #9 May 18 2021 06:22:37
%S A344393 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,
%T A344393 1191,302,1,1,502,4293,2416,57,0,1,1013,14608,15619,1191,1,1,2036,
%U A344393 47840,88234,15619,120,0,1,4083,152637,455192,156190,4293,1
%N A344393 T(n, k) = Eulerian1(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
%C A344393 The antidiagonal representation of the first order Eulerian numbers (A173018).
%e A344393 Triangle starts:
%e A344393 [ 0] [1]
%e A344393 [ 1] [1]
%e A344393 [ 2] [1,    0]
%e A344393 [ 3] [1,    1]
%e A344393 [ 4] [1,    4,     0]
%e A344393 [ 5] [1,   11,     1]
%e A344393 [ 6] [1,   26,    11,     0]
%e A344393 [ 7] [1,   57,    66,     1]
%e A344393 [ 8] [1,  120,   302,    26,    0]
%e A344393 [ 9] [1,  247,  1191,   302,    1]
%e A344393 [10] [1,  502,  4293,  2416,   57, 0]
%e A344393 [11] [1, 1013, 14608, 15619, 1191, 1]
%p A344393 T := (n, k) -> combinat:-eulerian1(n - k, k):
%p A344393 seq(print(seq(T(n, k), k=0..n/2)), n = 0..11);
%Y A344393 Cf. A000800 (row sums).
%Y A344393 Cf. A173018.
%K A344393 nonn,tabf
%O A344393 0,8
%A A344393 _Peter Luschny_, May 17 2021