A027447 - OEIS

%I #27 Nov 06 2019 18:19:36

%S 1,7,1,85,19,4,415,115,37,9,12019,3799,1489,549,144,13489,4669,2059,

%T 919,364,100,726301,268921,128431,64171,30676,12700,3600,3144919,

%U 1227199,621139,334699,178669,89125,38025,11025,30300391,12335311,6527971,3714811,2134141,1187125,609625,265825,78400

%N Triangle read by rows: cube of the lower triangular mean matrix.

%F Let A be the matrix with A[i,j] = 1/i if j <= i, 0 if j > i. Then this table lists the numerators in A^3 when each row is written using the least common denominator. [Edited by _M. F. Hasler_, Nov 05 2019]

%e Triangle begins:

%e       1;

%e       7,    1;

%e      85,   19,    4;

%e     415,  115,   37,   9;

%e   12019, 3799, 1489, 549, 144,

%e   ...

%t rows = 9; m = Table[ If[j <= i, 1/i, 0], {i, 1, rows}, {j, 1, rows}]; m3 = m.m.m; Table[ fracs = m3[[i]]; nums = fracs // Numerator; dens = fracs // Denominator; lcm = LCM @@ dens; Table[ nums[[j]]*lcm/dens[[j]], {j, 1, i}], {i, 1, rows}] // Flatten (* _Jean-François Alcover_, Mar 05 2013 *)

%o (PARI) tabl(nn) = {my(M = matrix(nn, nn, i, j, if (j<=i, 1/i, 0))^3); for (n=1, nn, my(row = M[n,1..n]); print(denominator(row)*row))} \\ _Michel Marcus_, Nov 05 2019, edited by _M. F. Hasler_, Nov 05 2019

%o (PARI) A027447_row(n)=denominator(n=(matrix(n,n, i,j, (j<=i)/i)^3)[n,])*n \\ _M. F. Hasler_, Nov 05 2019

%Y Cf. A027446, A027448.

%K nonn,tabl

%O 1,2

%A _Olivier Gérard_

%E More terms from _Michel Marcus_, Nov 05 2019