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A027517
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Cube of the lower triangular normalized partition matrix.
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6
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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
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..34.
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A008284.
Sequence in context: A100254 A119935 A027447 * A092082 A013559 A051186
Adjacent sequences: A027514 A027515 A027516 * A027518 A027519 A027520
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KEYWORD
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nonn,tabl
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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