A027518 4th power of the lower triangular normalized partition matrix.

1, 15, 1, 575, 65, 8, 28759, 4393, 544, 54, 26454859, 4978093, 871144, 95904, 13500, 35854425017, 7684637159, 1436323472, 190754352, 27540000, 3087000, 141598322427, 34558204013, 7383254904, 1130247120, 197499248, 24685024

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

Numerators of lower triangle of (a[i, j])^4 where a[i, j] = A008284(i, j) / Partitions(i) if j<=i, 0 if j>i.

Mathematica

rows = 7; m =  Table[If[k <= n, Length[IntegerPartitions[n, {k}]]/PartitionsP[n],    0], {n, 1, rows}, {k, 1, rows}]; m4 = m.m.m.m; Table[fracs = m4[[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: A049224 A223517 A027448 * A027539 A027479 A027497

Adjacent sequences: A027515 A027516 A027517 * A027519 A027520 A027521

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved