%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