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A027448
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Triangle read by rows: 4th power of the lower triangular mean matrix (M[i,j] = 1/i for i <= j).
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11
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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EXAMPLE
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Table starts:
1
15 1
575 65 8
5845 865 175 27
874853 153713 39743 9963 1728
1009743 200403 60333 19153 5368 1000
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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