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%I #9 Nov 20 2022 10:52:56
%S 1,1,1,1,3,2,1,7,14,6,1,15,70,70,28,1,31,310,930,868,204,1,63,1302,
%T 8370,18228,12852,2344
%N Eigentriangle of triangle A022166.
%C An eigentriangle of triangle T may be defined by taking the termwise product of row n-1 of T and the first n terms of the eigensequence of T; 0<=k<=n.
%C Row sums = A125812 shifted 1 place to the left: (1, 2, 6, 28, 204,...).
%C Sum of n-th row terms = rightmost term of (n+1)-th row.
%C 1, 1;
%C 1, 3, 1;
%C 1, 7, 7, 1;
%C 1, 15, 35, 15, 1;
%C ... (and the eigensequence of A022166 = A125812: (1, 1, 2, 6, 28, 204,...) we apply the termwise product of (n-1)-th row of A022166 and the first n terms of A125812.
%F Given triangle A022166: 1;
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 3, 2;
%e 1, 7, 14, 6;
%e 1, 15, 70, 90, 28;
%e 1, 31, 310, 930, 868, 204;
%e ...
%e Row 3 of A022166 = (1, 7, 7, 1), first 4 terms of A143774 = (1, 1, 2, 6), so row 3 of A143774 = (1*1, 7*1, 7*2, 1*6) = (1, 7, 14, 6).
%Y Cf. A022166, A125812.
%K nonn,tabl,more
%O 0,5
%A _Gary W. Adamson_, Aug 31 2008
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