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A128089 Denominators in inverse of triangle A128078 by rows, n * each term in n-th row of A126615. 0

%I #7 Feb 15 2022 07:49:36

%S 1,4,4,6,18,9,8,24,48,16,10,30,60,100,25,12,36,72,120,180,36,14,42,84,

%T 140,210,294,49,16,48,96,160,240,336,448,64,18,54,108,180,270,378,504,

%U 648,81,20,60,120,200,300,420,560,720,900,100

%N Denominators in inverse of triangle A128078 by rows, n * each term in n-th row of A126615.

%C Row sums = A014820: (1, 8, 33, 96, 225, 456, ...).

%C Denominators of the inverse of A128078: (1/1; 1/4, 1/4; 1/6, 1/18, 1/9; 1/8, 1/24, 1/48, 1/16; ...).

%C Row sums of this triangle: 1/1, 1/2, 1/3, ...; e.g., (1/8 + 1/24 + 1/48 + 1/16) = 1/4.

%F Denominators in inverse triangular matrix of A128078, where A128078 = A002260 * A128064, = (1; -1, 4; -1, -2, 9; -1, -2, -3, 16; ...).

%e First few rows of the triangle:

%e 1;

%e 4, 4;

%e 6, 18, 9;

%e 8, 24, 48, 16;

%e 10, 30, 60, 100, 25;

%e 12, 36, 72, 120, 180, 36;

%e 14, 42, 84, 140, 210, 294, 49;

%e 16, 48, 96, 160, 240, 336, 448, 64;

%e ...

%e Row 4 = (8, 24, 48, 16) = 4 * (2, 6, 12, 4); where (2, 6, 12, 4) = row 4 of A126615.

%Y Cf. A128078, A014820, A006527, A126615, A002260, A128064.

%K nonn,tabl,frac

%O 1,2

%A _Gary W. Adamson_, Feb 14 2007

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