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%I #5 Feb 13 2022 18:05:44
%S 1,1,2,6,8,24,8,120,16,720,48,64,5040,192,64,40320,960,128,362880,
%T 5760,384,512,3628800,40320,1536,512,39916800,322560,7680,1024,
%U 479001600,2903040,46080,3072,4096,6227020800,29030400,322560,12288,4096
%N T(n, k) = 2^(3*k)*(n - 3*k)!, for n >= 0 and 0 <= k <= floor(n/3). Triangle read by rows.
%e [ 0] 1;
%e [ 1] 1;
%e [ 2] 2;
%e [ 3] 6, 8;
%e [ 4] 24, 8;
%e [ 5] 120, 16;
%e [ 6] 720, 48, 64;
%e [ 7] 5040, 192, 64;
%e [ 8] 40320, 960, 128;
%e [ 9] 362880, 5760, 384, 512;
%e [10] 3628800, 40320, 1536, 512;
%e [11] 39916800, 322560, 7680, 1024;
%e [12] 479001600, 2903040, 46080, 3072, 4096;
%p T := (n, k) -> 2^(3*k)*(n-3*k)!: seq(seq(T(n,k), k = 0..n/3), n = 0..13);
%t Table[2^(3k) (n-3k)!,{n,0,20},{k,0,Floor[n/3]}]//Flatten (* _Harvey P. Dale_, Feb 13 2022 *)
%Y Cf. A000142, A138230.
%K nonn,tabf
%O 0,3
%A _Peter Luschny_, Jun 06 2021
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