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Triangle read by rows: M*Q, where M = an infinite lower triangular matrix with A140456 in every column: (1, 1, 1, 3, 7, 23, 71, ...) and Q = a matrix with A000085 as the main diagonal the rest zeros.
1

%I #4 Feb 08 2022 23:23:38

%S 1,1,1,1,1,2,3,1,2,4,7,3,2,4,10,23,7,6,4,10,26,71,23,14,12,10,26,76,

%T 255,71,46,28,30,26,76,232,911,255,142,92,70,78,76,232,764,3535,911,

%U 510,284,230,182,228,232,764,2620

%N Triangle read by rows: M*Q, where M = an infinite lower triangular matrix with A140456 in every column: (1, 1, 1, 3, 7, 23, 71, ...) and Q = a matrix with A000085 as the main diagonal the rest zeros.

%C An eigentriangle.

%C Row sums = A000085 starting with offset 1.

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

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 1, 1, 2;

%e 3, 1, 2, 4;

%e 7, 3, 2, 4, 10;

%e 23, 7, 6, 4, 10, 26;

%e 71, 23, 14, 12, 10, 26, 76;

%e 255, 71, 46, 28, 30, 26, 76, 232;

%e 911, 255, 142, 92, 70, 78, 76, 232, 764;

%e 3535, 911, 510, 284, 230, 182, 228, 232, 764, 2620;

%e 13903, 3535, 1822, 1020, 710, 598, 532, 696, 764, 2620, 9496;

%e ...

%e Row r = (3, 1, 2, 4) = (3*1, 1*1, 1*2, 1*4) = termwise products of (3, 1, 1, 1) and (1, 1, 2, 4), where A000085 = (1, 1, 2, 4, 10, 26, 76, ...).

%Y Cf. A000085, A140456.

%K eigen,nonn,tabl

%O 1,6

%A _Gary W. Adamson_, Dec 12 2008