A208057 Triangle by rows, generated from the odd integers and related to A000165.

1, 1, 1, 4, 3, 1, 24, 18, 5, 1, 192, 144, 40, 7, 1, 1920, 1440, 400, 70, 9, 1, 23040, 17280, 4800, 840, 108, 11, 1, 322560, 241920, 67200, 11760, 1512, 154, 13, 1, 5160960, 3870720, 1075200, 188160, 24192, 2464, 208, 15, 1

Offset: 0

Author

Gary W. Adamson, Feb 22 2012

Keywords

• nonn
• tabl

Comments

Row sums = A000165, the double factorial numbers: (1, 2, 8, 48, 384,...).

Left border = A002866 and the eigensequence of the odd integers prefaced with a 1.

Examples

			First few rows of the triangle:
  1;
  1, 1;
  4, 3, 1;
  24, 18, 5, 1;
  192, 144, 40, 7, 1;
  1920, 1440, 400, 70, 9, 1;
  23040, 17280, 4800, 840, 108, 11, 1;
  322560, 241920, 67200, 11760, 1512, 154, 13, 1;
  ...
		

Links

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

Crossrefs

Cf. A000165, A002866, A158405.

Programs

Maple

T:= proc(n) option remember; local M;
      M:= (Matrix(n+1, (i, j)-> `if`(i=j, 1, `if`(i>j, -2*j+1, 0)))^(-1));
      seq(M[n+1, k], k=1..n+1)
    end:
seq(T(n), n=0..10);  # Alois P. Heinz, Feb 27 2012

Mathematica

T[n_] := T[n] = Module[{M}, M = Table[If[i == j, 1, If[i>j, -2*j+1, 0]], {i, 1, n+1 }, {j, 1, n+1}] // Inverse; M[[n+1]]]; Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)

Formula

Eigentriangle of triangle A158405 (odd integers in every row: (1, 3, 5,...)); the inverse of:

1;

-1, 1;

-1, -3, 1;

-1, -3, -5, 1;

-1, -3, -5, -7, 1;

...

Extensions

Typo in term 17 corrected by Alois P. Heinz, Dec 06 2012