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.
LINKS
Wolfdieter Lang, First ten rows and rationals.
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
KEYWORD
AUTHOR
Wolfdieter Lang, Jul 20 2006
EXTENSIONS
Offset corrected by R. J. Mathar, Nov 05 2019
STATUS
approved