A027447 Triangle read by rows: cube of the lower triangular mean matrix.

1, 7, 1, 85, 19, 4, 415, 115, 37, 9, 12019, 3799, 1489, 549, 144, 13489, 4669, 2059, 919, 364, 100, 726301, 268921, 128431, 64171, 30676, 12700, 3600, 3144919, 1227199, 621139, 334699, 178669, 89125, 38025, 11025, 30300391, 12335311, 6527971, 3714811, 2134141, 1187125, 609625, 265825, 78400

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

Let A be the matrix with A[i,j] = 1/i if j <= i, 0 if j > i. Then this table lists the numerators in A^3 when each row is written using the least common denominator. [Edited by M. F. Hasler, Nov 05 2019]

Example

Triangle begins:
      1;
      7,    1;
     85,   19,    4;
    415,  115,   37,   9;
  12019, 3799, 1489, 549, 144,
  ...

Mathematica

rows = 9; m = Table[ If[j <= i, 1/i, 0], {i, 1, rows}, {j, 1, rows}]; m3 = m.m.m; Table[ fracs = m3[[i]]; nums = fracs // Numerator; dens = fracs // Denominator; lcm = LCM @@ dens; Table[ nums[[j]]*lcm/dens[[j]], {j, 1, i}], {i, 1, rows}] // Flatten (* Jean-François Alcover, Mar 05 2013 *)

Prog

(PARI) tabl(nn) = {my(M = matrix(nn, nn, i, j, if (j<=i, 1/i, 0))^3); for (n=1, nn, my(row = M[n, 1..n]); print(denominator(row)*row))} \\ Michel Marcus, Nov 05 2019, edited by M. F. Hasler, Nov 05 2019
(PARI) A027447_row(n)=denominator(n=(matrix(n, n, i, j, (j<=i)/i)^3)[n, ])*n \\ M. F. Hasler, Nov 05 2019

Crossrefs

Cf. A027446, A027448.

Sequence in context: A110788 A100254 A119935 * A027517 A092082 A013559

Adjacent sequences: A027444 A027445 A027446 * A027448 A027449 A027450

Keyword

nonn,tabl

Author

Olivier Gérard

Extensions

More terms from Michel Marcus, Nov 05 2019

Status

approved