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

Author

Olivier Gérard

Keywords

• nonn
• tabl

Examples

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

Crossrefs

Cf. A027446, A027448.

Programs

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 *)

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

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]

Extensions

More terms from Michel Marcus, Nov 05 2019