A155453 Triangle read by rows: T(n,k) = 1 + n! - k! - (n - k)! + k!*(n - k)!.

1, 1, 1, 2, 2, 2, 6, 6, 6, 6, 24, 24, 25, 24, 24, 120, 120, 125, 125, 120, 120, 720, 720, 743, 745, 743, 720, 720, 5040, 5040, 5159, 5155, 5155, 5159, 5040, 5040, 40320, 40320, 41039, 40915, 40849, 40915, 41039, 40320, 40320, 362880, 362880, 367919, 366475, 365617, 365617, 366475, 367919, 362880, 362880

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Example

Triangle begins:
     1;
     1,    1;
     2,    2,    2;
     6,    6,    6,    6;
    24,   24,   25,   24,   24;
   120,  120,  125,  125,  120,  120;
   720,  720,  743,  745,  743,  720,  720;
  5040, 5040, 5159, 5155, 5155, 5159, 5040, 5040;
  ...

Mathematica

Table[Table[1 - (k! - n! + (-k + n)! - k!*(n - k)!), {k, 0, n}], {n, 0, 10}];
Flatten[%]

Prog

(PARI) T(n, k) = 1 + n! - k! - (n - k)! + k!*(n - k)! \\ Andrew Howroyd, Nov 19 2025

Crossrefs

Sequence in context: A395725 A080969 A214078 * A032558 A211512 A139552

Adjacent sequences: A155450 A155451 A155452 * A155454 A155455 A155456

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Jan 22 2009

Status

approved