1,4

As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

Row sums = A006973 starting (1, 2, 9, 24, 130, 720, 8505, 35840,...).

Left border = A156791: (1, 1, 6, 7, 78, 420, 6872,...).

Triangle read by rows, T(n,k) = M*Q =(A156791(n-k+1) * (A006973 * 0^(n-k)))

M = an infinite lower triangular matrix with A156791: (1, 1, 6, 7, 78,...) in

every column.

Q = an infinite lower triangular matrix with A006973 prefaced with a 1

as the main diagonal: (1, 1, 2, 9, 24, 130, 720, 8505,...) and the rest zeros.

First few rows of the triangle =

1,

1, 1;

6, 1, 2;

7, 6, 2, 9;

78, 7, 12, 9, 24;

420, 78, 14 54, 24, 130;

6872, 420, 156, 63, 144, 130, 720;

17253, 6872, 840, 702, 168, 780, 720, 8505;

326552, 17253, 13744, 3780, 1872, 910, 4320, 8505, 35840;

...

Example: Row 4 = (7, 6, 2, 9) = termwise products of (7, 6, 1, 1) and (1, 1, 2, 9).

Cf. A156791, A006973

Sequence in context: A085766 A002329 A053453 this_sequence A021624 A021066 A082730

Adjacent sequences: A156789 A156790 A156791 this_sequence A156793 A156794 A156795

eigen,nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 15 2009