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A344392 T(n, k) = k!*Stirling2(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.

%I A344392 #12 May 18 2021 07:26:25
%S A344392 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,
%T A344392 240,0,1,254,1806,1560,120,0,1,510,5796,8400,1800,0,1,1022,18150,
%U A344392 40824,16800,720,0,1,2046,55980,186480,126000,15120
%N A344392 T(n, k) = k!*Stirling2(n - k, k), for n >= 0 and 0 <= k <= floor(n/2). Triangle read by rows.
%C A344392 The antidiagonal representation of the Fubini numbers (A131689).
%e A344392 Triangle starts:
%e A344392 [ 0] [1]
%e A344392 [ 1] [0]
%e A344392 [ 2] [0, 1]
%e A344392 [ 3] [0, 1]
%e A344392 [ 4] [0, 1, 2]
%e A344392 [ 5] [0, 1, 6]
%e A344392 [ 6] [0, 1, 14, 6]
%e A344392 [ 7] [0, 1, 30, 36]
%e A344392 [ 8] [0, 1, 62, 150, 24]
%e A344392 [ 9] [0, 1, 126, 540, 240]
%e A344392 [10] [0, 1, 254, 1806, 1560, 120]
%e A344392 [11] [0, 1, 510, 5796, 8400, 1800]
%p A344392 T := (n, k) -> k!*Stirling2(n - k, k):
%p A344392 seq(seq(T(n, k), k=0..n/2), n = 0..11);
%Y A344392 Cf. A105795 (row sums).
%Y A344392 Cf. A019538, A131689, A048993.
%K A344392 nonn,tabf
%O A344392 0,9
%A A344392 _Peter Luschny_, May 17 2021