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A143778 Eigentriangle of A001263, the Narayana triangle. 1

%I

%S 1,1,1,1,3,2,1,6,12,6,1,10,40,60,25,1,15,100,300,375,136,1,21,210,

%T 1050,2625,2856,927,1,18,392,2940,12250,26656,25956,7690,1,36,672,

%U 7056,44100,15993,311472,276840,75913

%N Eigentriangle of A001263, the Narayana triangle.

%C The Narayana triangle begins:

%C 1;

%C 1, 1;

%C 1, 3, 1;

%C 1, 6, 6, 1;

%C 1, 10, 20, 10, 1;

%C ...

%C 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,...).

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

%C Right border of the triangle = the eigensequence of T.

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

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

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

%F Apparently for k<n, a(n,k)= binomial(n+1,k+1)*n!/(n+1-k)!. - _Tom Copeland_, Oct 08 2014

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 3, 2;

%e 1, 6, 12, 6;

%e 1, 10, 40, 60, 25;

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

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

%e ...

%e 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).

%Y Cf. A001263, A102812.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Aug 31 2008

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)