A119948 - OEIS

%I #13 Nov 06 2019 01:59:41

%S 1,4,4,18,18,9,48,48,48,16,300,300,300,100,25,120,120,120,360,180,36,

%T 980,980,980,2940,1470,294,49,2240,2240,2240,6720,6720,1344,448,64,

%U 22680,22680,22680,22680,22680,4536

%N Triangle of denominators in the square of the matrix with A[i,j] = 1/i for j <= i, 0 otherwise.

%C The triangle of the corresponding numerators is A119947. The rationals appear in lowest terms.

%C The least common multiple (LCM) of row i gives [1, 4, 18, 48, 300, 360, 2940, 6720, 22680, ...], which coincides with A081528.

%F T(i,j) = denominator((A^2)[i,j]), where the lower triangular matrix A has elements a[i,j] = 1/i if j <= i, 0 if j > i.

%e The first rows of the table are:

%e   [1];

%e   [4, 4];

%e   [18, 18, 9];

%e   [48, 48, 48, 16];

%e   [300, 300, 300, 100, 25];

%e   [120, 120, 120, 360, 180, 36]; ...

%o (PARI) A119948_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^2); vector(n, r, apply(denominator, M[r, 1..r]))} \\ _M. F. Hasler_, Nov 05 2019

%Y Row sums give A119950. Row sums of the triangle of rationals always give 1.

%K nonn,easy,frac,tabl

%O 1,2

%A _Wolfdieter Lang_, Jul 20 2006

%E Edited by _M. F. Hasler_, Nov 05 2019