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 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 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 STATUS approved

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Last modified December 6 14:47 EST 2019. Contains 329806 sequences. (Running on oeis4.)