0,5

The Narayana triangle begins:

1;

1, 1;

1, 3, 1;

1, 6, 6, 1;

1, 10, 20, 10, 1;

...

An eigentriangle of T is generated by taking the termwise product of (n-1)-th row terms of triangle T (in this case the Narayana triangle A001263); and the eigensequence of T = A102812 = (1, 1, 2, 6, 25, 136, 927,...).

Sum of n-th row terms of triangle A143778 = rightmost term of (n+1)-th row.

Right border of the triangle = the eigensequence of T.

Row sums of the triangle = the eigensequence of T shifted one place to the left: (1, 2, 6, 25, 136,...)

(A102812 * 0^(n-k)) = an infinite lower triangular matrix with A102812 as the main diagonal and the rest zeros.

First few rows of the triangle =

1;

1, 1;

1, 3, 2;

1, 6, 12, 6;

1, 10, 40, 60, 25;

1, 15, 100, 300, 375, 136;

1, 21, 210, 1050, 2625, 2856, 927;

...

Row 3 = (1, 6, 12, 6) = (1*1, 6*1, 6*2, 1*6) = termwise product of row 3 of the Narayana triangle: (1, 6, 6, 1) and the first 4 terms of the eigensequence of the Narayana triangle = (1, 1, 2, 6).

Triangle read by rows, A001263 * (A102812 * 0^(n-k)); 0<=k<=n

A001263, Cf. A102812

Sequence in context: A156367 A008276 A094638 this_sequence A164645 A115755 A016556

Adjacent sequences: A143775 A143776 A143777 this_sequence A143779 A143780 A143781

nonn,tabl

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