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%I #12 Nov 07 2019 04:48:00
%S 1,15,1,575,65,8,28759,4393,544,54,26454859,4978093,871144,95904,
%T 13500,35854425017,7684637159,1436323472,190754352,27540000,3087000,
%U 141598322427,34558204013,7383254904,1130247120,197499248,24685024
%N 4th power of the lower triangular normalized partition matrix.
%F Numerators of lower triangle of (a[i, j])^4 where a[i, j] = A008284(i, j) / Partitions(i) if j<=i, 0 if j>i.
%t rows = 7; m = Table[If[k <= n, Length[IntegerPartitions[n, {k}]]/PartitionsP[n], 0], {n, 1, rows}, {k, 1, rows}]; m4 = m.m.m.m; Table[fracs = m4[[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_