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A208057 Triangle by rows, generated from the odd integers and related to A000165. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Mar 09 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A000165, A002866, A158405.

Sequence in context: A181355 A128320 A189507 * 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

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)