0,9

Sum of n-th row terms = rightmost nonzero term of next row.

Row sums = the partition numbers, A000041, as well as the rightmost diagonal with no zeros.

Triangle read by rows, termwise products of A000041 (the partition numbers); and the partition number generator, A145006.

First few rows of the triangle =

1;

1, 0;

1, 1, 0;

0, 1, 2, 0;

0, 0, 2, 3, 0;

-1, 0, 0, 3, 5, 0;

0, -1, 0, 0, 5, 7, 0;

-1, 0, -2, 0, 0, 7, 11, 0,;

0, -1, 0, -3, 0, 0, 11, 15, 0;

0, 0, -2, 0, -5, 0, 0, 15, 22, 0;

0, 0, 0, -3, 0, -7, 0, 0, 22, 30, 0;

0, 0, 0, 0, -5, 0, -11, 0, 0, 30, 42, 0;

1, 0, 0, 0, 0, -7, 0, -15, 0, 0, 42, 56, 0;

0, 1, 0, 0, 0, 0, -11, 0, -22, 0, 0, 56, 77, 0;

0, 0, 2, 0, 0, 0, 0, -15, 0, -30, 0, 0, 77, 101, 0;

...

Example: row 4 = (0, 0, 2, 3) = termwise products of (0, 0, 1, 1) and (1, 1, 2, 3), where (0, 0, 1, 1) = row 4 of triangle A145006. The partition numbers = (1, 1, 2, 3, 5, 7, 11, 15,...).

Sequence in context: A057108 A063958 A126164 this_sequence A151670 A153587 A059286

Adjacent sequences: A145004 A145005 A145006 this_sequence A145008 A145009 A145010

eigen,tabl,sign

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 28 2008