A143778 Eigentriangle of A001263, the Narayana 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, 1, 18, 392, 2940, 12250, 26656, 25956, 7690, 1, 36, 672, 7056, 44100, 15993, 311472, 276840, 75913

Offset

0,5

Comments

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.

Links

Table of n, a(n) for n=0..44.

Formula

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

Apparently for k<n, a(n,k)= binomial(n+1,k+1)*n!/(n+1-k)!. - Tom Copeland, Oct 08 2014

Example

Triangle begins:
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).

Crossrefs

Cf. A001263, A102812.

Sequence in context: A196844 A196843 A367023 * A200536 A164645 A115755

Adjacent sequences: A143775 A143776 A143777 * A143779 A143780 A143781

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 31 2008

Status

approved