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A119935
Triangle of numerators of the cube of a certain lower triangular matrix.
5
1, 7, 1, 85, 19, 1, 415, 115, 37, 1, 12019, 3799, 1489, 61, 1, 13489, 4669, 2059, 919, 91, 1, 726301, 268921, 128431, 64171, 7669, 127, 1, 3144919, 1227199, 621139, 334699, 178669, 3565, 169, 1, 30300391
OFFSET
1,2
COMMENTS
The triangle of the corresponding denominators is A119932.
This triangle of numerators is related to (and was derived from) A027447. There the least common multiple (lcm) of the denominators of each row i of the triangle of rationals r(i,j) has been multiplied in order to obtain an integer triangle.
FORMULA
a(i,j) = numerator(r(i,j)) with r(i,j):=(A^3)[i,j], where the lower triangular matrix A has elements a[i,j] = 1/i if j<=i, 0 if j>i.
MAPLE
A119935 := proc(n::integer, k::integer)
m := Matrix(n, n) ;
for i from 1 to n do
for j from 1 to i do
m[i, j] := 1/i ;
end do:
end do:
m3 := LinearAlgebra[MatrixPower](m, 3) ;
m3[n, k] ;
numer(%) ;
end proc: # R. J. Mathar, Nov 05 2019
PROG
(NARS2000) {d↑⍨¯1+(d←⍕⍵)⍳'r'}¨(c≠0)/c←, b+.×b+.×b←a∘.{⍺÷⍨⍺≥⍵}a←⍳20x ⍝ Michael Turniansky, Jan 11 2021
CROSSREFS
a(i, j)=1/A002024(i, j), i>=1, j<=i.
Row sums give A119934. Row sums of the triangle of rationals are identical 1.
Cf. A027447.
Sequence in context: A221367 A110788 A100254 * A027447 A027517 A092082
KEYWORD
nonn,easy,tabl,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
EXTENSIONS
Offset corrected by R. J. Mathar, Nov 05 2019
STATUS
approved