OFFSET
1,6
COMMENTS
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 A125653 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).
EXAMPLE
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;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Aug 31 2008
STATUS
approved