A027538 Cube of the lower triangular normalized Eulerian number matrix.
1, 7, 1, 163, 52, 1, 8873, 4719, 231, 1, 930581, 731646, 64966, 806, 1, 166430695, 180969681, 25235006, 610166, 2451, 1, 46667364787, 67248150516, 13560308427, 543687292, 4546137, 6840, 1, 19297882224241, 35761409868799, 9882496297869
Offset: 1
Crossrefs
Cf. A008292.
Programs
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Mathematica
rows = 8; t[n_, k_] := Sum[(-1)^j*(k - j)^n*Binomial[n + 1, j], {j, 0, k}]; m = Table[If[k <= n, t[n, k]/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 *)
Formula
Numerators of lower triangle of (a[ i, j ])^3 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i