A027448 Triangle read by rows: 4th power of the lower triangular mean matrix (M[i,j] = 1/i for i <= j).
1, 15, 1, 575, 65, 8, 5845, 865, 175, 27, 874853, 153713, 39743, 9963, 1728, 1009743, 200403, 60333, 19153, 5368, 1000, 389919909, 84873489, 28400079, 10419739, 3681784, 1105000, 216000, 3449575767, 807843807, 292420227
Offset: 1
Examples
Table starts:
1
15 1
575 65 8
5845 865 175 27
874853 153713 39743 9963 1728
1009743 200403 60333 19153 5368 1000
Links
- Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
Programs
-
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 *) -
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
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
Extensions
Edited by Robert Israel, Oct 05 2019