A027516 Square of the lower triangular normalized partition matrix.

1, 3, 1, 11, 5, 2, 38, 26, 8, 3, 316, 247, 121, 36, 15, 3183, 2971, 1508, 558, 180, 70, 11265, 11729, 7032, 2928, 1178, 364, 154, 14759, 17212, 10541, 5127, 2033, 784, 259, 105, 17862, 22396, 15648, 7593, 3596, 1379, 567, 182, 77, 22567, 30830

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Formula

Numerators of lower triangle of (a[i, j])^2 where a[i, j] = A008284(i, j) / Partitions(i) if j<=i, 0 if j>i.

Mathematica

rows = 10; m = Table[If[k <= n, Length[IntegerPartitions[n, {k}]]/PartitionsP[n], 0], {n, 1, rows}, {k, 1, rows}]; m2 = m.m; Table[fracs = m2[[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: A119947 A165674 A027446 * A092808 A343171 A113955

Adjacent sequences: A027513 A027514 A027515 * A027517 A027518 A027519

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved