1,6

An eigentriangle of triangle T is generated by taking the termwise product row (n-1) of T and the first n terms of the eigensequence of T. Here T = A125653 and the eigensequence of T = A125654. The operation (A125654 * 0^(n-k)) creates an infinite lower triangular matrix with A125654 as the main diagonal and the rest zeros:

1;

0, 2;

0, 0, 4;

0, 0, 0, 9;

0, 0, 0, 0, 24;

..., where A125654 = (1, 1, 2, 4, 9, 24, 75, 269,...).

Triangle A143775 begins:

1;

1, 1;

1, 1, 1;

1, 2, 1, 1;

1, 4, 3, 1, 1;

... Row sums = A125654 (column 1) shifted one place to the left: (1, 2, 4, 9, 24, 75,...).

Sum of row n terms = rightmost term of row (n+1).

First few rows of the triangle = 1;

1, 1;

1, 1, 2;

1, 2, 2, 4;

1, 4, 6, 4, 9;

1, 9, 16, 16, 9, 24;

1, 24, 48, 52, 45, 24, 75;

1, 75, 168, 188, 171, 144, 75, 269;

... Row 4 = (1, 4, 6, 4, 9) = termwise product of row 4 of triangle A143775: (1, 4, 3, 1, 1) and the first 5 terms of A125654: (1, 1, 2, 4, 9) = (1*1, 4*1, 3*2, 1*4, 1*9).

Triangle read by rows, A125653 * (A125654 * 0^(n-k)); 0<=k<=n

A125653, Cf. A125654

Sequence in context: A062790 A046640 A049823 this_sequence A003165 A158379 A122838

Adjacent sequences: A143772 A143773 A143774 this_sequence A143776 A143777 A143778

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 31 2008