A344914 T(n, k) = 2^(3*k)*(n - 3*k)!, for n >= 0 and 0 <= k <= floor(n/3). Triangle read by rows.

1, 1, 2, 6, 8, 24, 8, 120, 16, 720, 48, 64, 5040, 192, 64, 40320, 960, 128, 362880, 5760, 384, 512, 3628800, 40320, 1536, 512, 39916800, 322560, 7680, 1024, 479001600, 2903040, 46080, 3072, 4096, 6227020800, 29030400, 322560, 12288, 4096

Offset: 0

Author

Peter Luschny, Jun 06 2021

Keywords

• nonn
• tabf

Examples

			[ 0] 1;
[ 1] 1;
[ 2] 2;
[ 3] 6,         8;
[ 4] 24,        8;
[ 5] 120,       16;
[ 6] 720,       48,      64;
[ 7] 5040,      192,     64;
[ 8] 40320,     960,     128;
[ 9] 362880,    5760,    384,   512;
[10] 3628800,   40320,   1536,  512;
[11] 39916800,  322560,  7680,  1024;
[12] 479001600, 2903040, 46080, 3072, 4096;
		

Crossrefs

Cf. A000142, A138230.

Programs

Maple

T := (n, k) -> 2^(3*k)*(n-3*k)!: seq(seq(T(n,k), k = 0..n/3), n = 0..13);

Mathematica

Table[2^(3k) (n-3k)!,{n,0,20},{k,0,Floor[n/3]}]//Flatten (* Harvey P. Dale, Feb 13 2022 *)