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

1,2

Links

Table of n, a(n) for n=1..31.

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

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 *)

Crossrefs

Cf. A008292.

Sequence in context: A012034 A138324 A052122 * A334394 A027478 A009792

Adjacent sequences: A027535 A027536 A027537 * A027539 A027540 A027541

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved