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

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.

Links

Table of n, a(n) for n=1..37.

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

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

Adjacent sequences: A119932 A119933 A119934 * A119936 A119937 A119938

Keyword

nonn,easy,tabl,frac

Author

Wolfdieter Lang, Jul 20 2006

Extensions

Offset corrected by R. J. Mathar, Nov 05 2019

Status

approved