A259334 Triangle read by rows: T(n,k) = k*(n-1)!*n^(n-k-1)/(n-k)!, 1 <= k <= n.

1, 1, 1, 3, 4, 2, 16, 24, 18, 6, 125, 200, 180, 96, 24, 1296, 2160, 2160, 1440, 600, 120, 16807, 28812, 30870, 23520, 12600, 4320, 720, 262144, 458752, 516096, 430080, 268800, 120960, 35280, 5040, 4782969, 8503056, 9920232, 8817984, 6123600, 3265920, 1270080, 322560, 40320

Offset: 1

Author

N. J. A. Sloane, Jun 25 2015

Keywords

• nonn
• tabl

Examples

			Triangle begins:
     1;
     1,    1;
     3,    4,    2;
    16,   24,   18,    6;
   125,  200,  180,   96,   24;
  1296, 2160, 2160, 1440,  600,  120;
  ...
		

Links

• F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.
• F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424. (Annotated scanned copy)
• F. A. Haight, Letter to N. J. A. Sloane, n.d.

Crossrefs

Diagonals include A000272, A089946, A000142.

Cf. A000435.

Programs

PARI

tabl(nn) = {for (n=1, nn, for (k=1, n, print1(k*(n-1)!*n^(n-k-1)/(n-k)!, ", ");); print(););} \\ Michel Marcus, Jun 26 2015

Formula

A000435(n) = Sum_{k=0..n-1} k*T(n,k). - David desJardins, Jan 22 2017

Extensions

More terms from Michel Marcus, Jun 26 2015