A119935 - OEIS

%I #20 Jan 22 2021 23:01:33

%S 1,7,1,85,19,1,415,115,37,1,12019,3799,1489,61,1,13489,4669,2059,919,

%T 91,1,726301,268921,128431,64171,7669,127,1,3144919,1227199,621139,

%U 334699,178669,3565,169,1,30300391

%N Triangle of numerators of the cube of a certain lower triangular matrix.

%C The triangle of the corresponding denominators is A119932.

%C 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 Wolfdieter Lang, <a href="/A119932/a119932.txt">First ten rows and rationals.</a>

%F 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 := proc(n::integer,k::integer)

%p     m := Matrix(n,n) ;

%p     for i from 1 to n do

%p     for j from 1 to i do

%p         m[i,j] := 1/i ;

%p     end do:

%p     end do:

%p     m3 := LinearAlgebra[MatrixPower](m,3) ;

%p     m3[n,k] ;

%p     numer(%) ;

%p end proc: # _R. J. Mathar_, Nov 05 2019

%o (NARS2000) {d↑⍨¯1+(d←⍕⍵)⍳'r'}¨(c≠0)/c←,b+.×b+.×b←a∘.{⍺÷⍨⍺≥⍵}a←⍳20x ⍝ _Michael Turniansky_, Jan 11 2021

%Y a(i, j)=1/A002024(i, j), i>=1, j<=i.

%Y Row sums give A119934. Row sums of the triangle of rationals are identical 1.

%Y Cf. A027447.

%K nonn,easy,tabl,frac

%O 1,2

%A _Wolfdieter Lang_, Jul 20 2006

%E Offset corrected by _R. J. Mathar_, Nov 05 2019