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A143778 Eigentriangle of A001263, the Narayana triangle. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A094638 A196844 A196843 * A200536 A164645 A115755

Adjacent sequences:  A143775 A143776 A143777 * A143779 A143780 A143781

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Aug 31 2008

STATUS

approved

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Last modified February 25 13:30 EST 2018. Contains 299654 sequences. (Running on oeis4.)