A208058 Triangle by rows relating to the factorials, generated from A002260.

1, 1, 1, 1, 2, 1, 2, 4, 3, 1, 6, 12, 9, 4, 1, 24, 48, 36, 16, 5, 1, 120, 240, 180, 80, 25, 6, 1, 720, 1440, 1080, 480, 150, 36, 7, 1, 5040, 10080, 7560, 3360, 1050, 252, 49, 8, 1, 40320, 80640, 60480, 26880, 8400, 2016, 392, 64, 9, 1

Offset: 0

Author

Gary W. Adamson, Feb 22 2012

Keywords

• nonn
• tabl

Comments

Row sums = A054091: (1, 2, 4, 10, 32, 130, 652,...)

Left border = the factorials, A000142 prefaced with a 1.

Examples

			First few rows of the triangle =
1;
1, 1;
1, 2, 1;
2, 4, 3, 1;
6, 12, 9, 4, 1;
24, 48, 36, 16, 5, 1;
120, 240, 180, 80, 25, 6, 1;
720, 1440, 1080, 480, 150, 36, 7, 1;
5040, 10080, 7560, 3360, 1050, 252, 49, 8, 1;
...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Cf. A000142, A002260, A054091.

Programs

Maple

T:= proc(n) option remember; local M, k;
      M:= Matrix(n+1, (i, j)->
                 `if`(i=j, 1, `if`(i>j, j*(-1)^(i+j), 0)))^(-1);
      seq(M[n+1, k], k=1..n+1)
    end:
seq(T(n), n=0..14);  # Alois P. Heinz, Feb 24 2012

Mathematica

T[n_] := T[n] = Module[{M}, M = Table[If[i == j, 1, If[i>j, j*(-1)^(i+j), 0]], {i, 1, n+1}, {j, 1, n+1}] // Inverse; M[[n+1]]]; Table[T[n], {n, 0, 14}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)

Formula

Inverse of:

1;

-1, 1;

1, -2, 1;

-1, 2, -3, 1;

1, -2, 3, -4, 1;

..., where triangle A002260 = (1; 1,2; 1,2,3;...)