0,8

A165490 is an eigentriangle (triangle A084938 * its shifted eigensequence),

having two distinct properties: row sums = A165489, the eigensequence of

triangle A084938: (1, 1, 2, 6, 23, 105, 550, 3236,...), and sum of row terms

= rightmost term of next row.

Triangle by rows, A084938 * its shifted eigensequence (1, 1, 1, 2, 6, 23,...)

diagonalized as an infinite lower triangular matrix:

1;

0, 1;

0, 0, 1;

0, 0, 0, 2;

0, 0, 0, 0, 6;

0, 0, 0, 0, 0, 23;

...

First few rows of the triangle =

1;

0, 1;

0, 1, 1;

0, 2, 2, 2;

0, 6, 5, 6, 6;

0, 24, 16, 18, 24, 23;

0, 120, 64, 62, 84, 115, 105;

0, 720, 312, 252, 312, 460, 630, 550;

0, 5040, 1812, 1212, 1302, 1840, 2835, 3850, 3236;

0, 40320, 12288, 6856, 6240, 7935, 12180, 19250, 25888, 21127;

...

Example: row 4 = (0, 6, 5, 6, 6) = termwise products of (0, 6, 5, 3, 1) and

(1, 1, 1, 2, 6)j; where (0, 6, 5, 3, 1) = row 4 of triangle A084938.

A084938, A165489

Sequence in context: A104241 A011139 A136663 this_sequence A131079 A078336 A076441

Adjacent sequences: A165487 A165488 A165489 this_sequence A165491 A165492 A165493

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2009