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A027516 Square of the lower triangular normalized partition matrix. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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 A113955 A110165

Adjacent sequences:  A027513 A027514 A027515 * A027517 A027518 A027519

KEYWORD

nonn,tabl,changed

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 18 09:55 EST 2019. Contains 329261 sequences. (Running on oeis4.)