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%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
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