A027517 Cube of the lower triangular normalized partition matrix.

1, 7, 1, 85, 19, 4, 814, 253, 49, 9, 102727, 38329, 10882, 1962, 450, 12277291, 5271157, 1581856, 346596, 74100, 14700, 46825417, 22745055, 7869040, 1965504, 512612, 100156, 23716, 65344835, 34733236, 12535613, 3543627, 948377, 226576

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Formula

Numerators of lower triangle of (a[i, j])^3 where a[i, j] = A008284(i, j) / Partitions(i) if j<=i, 0 if j>i.

Mathematica

rows = 8; m = Table[If[k <= n, Length[IntegerPartitions[n, {k}]]/PartitionsP[n], 0], {n, 1, rows}, {k, 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 *)

Crossrefs

Cf. A008284.

Sequence in context: A100254 A119935 A027447 * A092082 A013559 A051186

Adjacent sequences: A027514 A027515 A027516 * A027518 A027519 A027520

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved