%I #22 Nov 06 2019 18:20:44

%S 1,15,1,575,65,8,5845,865,175,27,874853,153713,39743,9963,1728,

%T 1009743,200403,60333,19153,5368,1000,389919909,84873489,28400079,

%U 10419739,3681784,1105000,216000,3449575767,807843807,292420227

%N Triangle read by rows: 4th power of the lower triangular mean matrix (M[i,j] = 1/i for i <= j).

%H Robert Israel, <a href="/A027448/b027448.txt">Table of n, a(n) for n = 1..10011</a> (rows 1 to 141, flattened)

%F Let M be the lower triangular matrix with entries M[i,j] = 1/i for 1<=j<=i, and B = M^4. Then a(i,j) = B(i,j)*lcm(denom(B(i,1)),...,denom(B(i,i))). - _Robert Israel_, Oct 05 2019

%F That is, the fractions in M^4 are written using the least common denominator before taking the numerators. - _M. F. Hasler_, Nov 05 2019

%e Table starts:

%e 1

%e 15 1

%e 575 65 8

%e 5845 865 175 27

%e 874853 153713 39743 9963 1728

%e 1009743 200403 60333 19153 5368 1000

%p Rows:= 10:

%p M:= Matrix(Rows,Rows,(i,j) -> `if`(i>=j,1/i,0)):

%p B:= M^4:

%p L:= [seq(ilcm(seq(denom(B[i,j]),j=1..i)),i=1..Rows)]:

%p seq(seq(B[i,j]*L[i],j=1..i),i=1..Rows); # _Robert Israel_, Oct 05 2019

%t rows = 8; m = Table[ If[j <= i, 1/i, 0], {i, 1, rows}, {j, 1, rows}]; m4 = m.m.m.m; Table[ fracs = m4[[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) A027448_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^4); vector(n,r,M[r,1..r]*denominator(M[r,1..r]))} \\ _M. F. Hasler_, Nov 05 2019

%Y Cf. A027446 (square of M), A027447 (cube of M).

%K nonn,tabl

%O 1,2

%A _Olivier Gérard_

%E Edited by _Robert Israel_, Oct 05 2019