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

0,4

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.

Links

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

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;

...

Example

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;
...

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 *)

Crossrefs

Cf. A000165, A002866, A158405.

Sequence in context: A189507 A348436 A350528 * A298673 A245732 A039621

Adjacent sequences: A208054 A208055 A208056 * A208058 A208059 A208060

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 22 2012

Extensions

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

Status

approved