A027539 4th power of the lower triangular normalized Eulerian number matrix.

1, 15, 1, 1135, 160, 1, 270505, 60335, 935, 1, 156871831, 49140396, 1343716, 4056, 1, 188025705967, 77463625233, 3230526398, 18687638, 14763, 1, 416173882222435, 216288860370444, 12659193075915, 119153175100

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

Numerators of lower triangle of (a[ i, j ])^4 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i

Mathematica

rows = 7; 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}]; 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 *)

Crossrefs

Cf. A008292.

Sequence in context: A223517 A027448 A027518 * A027479 A027497 A040221

Adjacent sequences: A027536 A027537 A027538 * A027540 A027541 A027542

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved