OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
FORMULA
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
That is, the fractions in M^4 are written using the least common denominator before taking the numerators. - M. F. Hasler, Nov 05 2019
EXAMPLE
Table starts:
1
15 1
575 65 8
5845 865 175 27
874853 153713 39743 9963 1728
1009743 200403 60333 19153 5368 1000
MAPLE
Rows:= 10:
M:= Matrix(Rows, Rows, (i, j) -> `if`(i>=j, 1/i, 0)):
B:= M^4:
L:= [seq(ilcm(seq(denom(B[i, j]), j=1..i)), i=1..Rows)]:
seq(seq(B[i, j]*L[i], j=1..i), i=1..Rows); # Robert Israel, Oct 05 2019
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by Robert Israel, Oct 05 2019
STATUS
approved