|
| |
|
|
A027517
|
|
Cube of the lower triangular normalized partition matrix.
|
|
6
|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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 ] = T(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
|
| |
|
|