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 A027516 Square of the lower triangular normalized partition matrix. 6

%I

%S 1,3,1,11,5,2,38,26,8,3,316,247,121,36,15,3183,2971,1508,558,180,70,

%T 11265,11729,7032,2928,1178,364,154,14759,17212,10541,5127,2033,784,

%U 259,105,17862,22396,15648,7593,3596,1379,567,182,77,22567,30830

%N Square of the lower triangular normalized partition matrix.

%F Numerators of lower triangle of (a[ i, j ])^2 where a[ i, j ] = T(i, j)/Partitions(i) if j<=i, 0 if j>i

%t 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 *)

%Y Cf. A008284.

%K nonn,tabl

%O 1,2

%A _Olivier Gérard_

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