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A119935 Triangle of numerators of the cube of a certain lower triangular matrix.

%I A119935 #20 Jan 22 2021 23:01:33
%S A119935 1,7,1,85,19,1,415,115,37,1,12019,3799,1489,61,1,13489,4669,2059,919,
%T A119935 91,1,726301,268921,128431,64171,7669,127,1,3144919,1227199,621139,
%U A119935 334699,178669,3565,169,1,30300391
%N A119935 Triangle of numerators of the cube of a certain lower triangular matrix.
%C A119935 The triangle of the corresponding denominators is A119932.
%C A119935 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.
%H A119935 Wolfdieter Lang, <a href="/A119932/a119932.txt">First ten rows and rationals.</a>
%F A119935 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.
%p A119935 A119935 := proc(n::integer,k::integer)
%p A119935     m := Matrix(n,n) ;
%p A119935     for i from 1 to n do
%p A119935     for j from 1 to i do
%p A119935         m[i,j] := 1/i ;
%p A119935     end do:
%p A119935     end do:
%p A119935     m3 := LinearAlgebra[MatrixPower](m,3) ;
%p A119935     m3[n,k] ;
%p A119935     numer(%) ;
%p A119935 end proc: # _R. J. Mathar_, Nov 05 2019
%o A119935 (NARS2000) {d↑⍨¯1+(d←⍕⍵)⍳'r'}¨(c≠0)/c←,b+.×b+.×b←a∘.{⍺÷⍨⍺≥⍵}a←⍳20x ⍝ _Michael Turniansky_, Jan 11 2021
%Y A119935 a(i, j)=1/A002024(i, j), i>=1, j<=i.
%Y A119935 Row sums give A119934. Row sums of the triangle of rationals are identical 1.
%Y A119935 Cf. A027447.
%K A119935 nonn,easy,tabl,frac
%O A119935 1,2
%A A119935 _Wolfdieter Lang_, Jul 20 2006
%E A119935 Offset corrected by _R. J. Mathar_, Nov 05 2019