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%I #8 Nov 20 2022 10:53:01
%S 1,1,1,1,4,2,1,13,26,7,1,40,260,280,47,1,121,2420,8470,5687,628
%N Eigentriangle of triangle A022167.
%C Row sums of the triangle = A125813 shifted one place to the left = (1, 2, 7, 47, 628,...).
%C Row sums of row n terms = rightmost term of row (n+1).
%C Example: rightmost term of row 3 = 7 = (1 + 4 + 2).
%C Triangle A022167 =
%C 1;
%C 1, 1;
%C 1, 4, 1;
%C 1, 13, 13, 1;
%C 1, 40, 130, 40, 1;
%C ... The eigensequence of A022167 = A125815: (1, 1, 2, 7, 47, 628, 17327,...).
%C Triangle A143777 applies a termwise product of the first n terms of (1, 1, 2, 7, 47,...) and the (n-1)-th row terms of triangle A022167.
%F Triangle read by rows, A022167 * (A125813 * 0^(n-k)); 0<=k<=n
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 4, 2;
%e 1, 13, 26, 7;
%e 1, 40, 260, 280, 47;
%e 1, 121, 2420, 8470, 5687, 628;
%e ...
%e Row 3 = (1, 13, 26, 7) = termwise product of (1, 13, 13, 1) and (1, 1, 2, 7); where (1, 13, 13, 1) = row 3 of triangle A022167 and (1, 1, 2, 7) = the first 4 terms of A125813, the eigensequence of A022167.
%Y Cf. A022167, A125813.
%K nonn,tabl,more
%O 0,5
%A _Gary W. Adamson_, Aug 31 2008
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