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

0,5

Comments

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

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

Links

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

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;...)

Example

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;
...

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 *)

Crossrefs

Cf. A000142, A002260, A054091.

Sequence in context: A179750 A091173 A101897 * A078142 A133422 A331136

Adjacent sequences: A208055 A208056 A208057 * A208059 A208060 A208061

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 22 2012

Status

approved