A144025 - OEIS

%I #4 Oct 20 2022 23:01:55

%S 1,1,1,2,1,2,4,2,2,5,9,4,4,5,13,21,9,8,10,13,35,51,21,18,20,26,35,96,

%T 127,51,42,45,52,70,96,267,323,127,102,105,117,140,192,267,750,835,

%U 323,254,255,273,315,384,534,720,2123,2188,835,646,635,663,735,864,1068

%N Eigentriangle by rows, A001006(n-k)*A005773(k); 0<=k<=n.

%C Left border = Motzkin numbers, A001006.

%C Right border = A005773.

%C Row sums = A005773 shifted: (1, 2, 5, 13, 35, 96, 267,...).

%C Sum of n-th row terms = rightmost term of next row.

%F Eigentriangle by rows, A001006(n-k)*A005773(k); 0<=k<=n.

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 2, 1, 2;

%e 4, 2, 2, 5;

%e 9, 4, 4, 5, 13;

%e 21, 9, 8, 10, 13, 35;

%e 51, 21, 18, 20, 26, 35, 96;

%e 127, 51, 42, 45, 52, 70, 96, 267;

%e 323, 127, 102, 105, 117, 140, 192, 267, 750;

%e 835, 323, 254, 255, 273, 315, 384, 534, 720, 2123;

%e ...

%e Row 3 = (4, 2, 2, 5) = termwise product of (4, 2, 1, 1) and the first 4 terms of A005773: (1, 1, 2, 5) = (4*1, 2*1, 1*2, 1*5). (4, 2, 1, 1) = the first 4 terms of A001066, reversed.

%Y Cf. A001066, A005773.

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Sep 07 2008