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%I #9 Mar 05 2013 09:12:14
%S 1,15,1,1135,160,1,270505,60335,935,1,156871831,49140396,1343716,4056,
%T 1,188025705967,77463625233,3230526398,18687638,14763,1,
%U 416173882222435,216288860370444,12659193075915,119153175100
%N 4th power of the lower triangular normalized Eulerian number matrix.
%F Numerators of lower triangle of (a[ i, j ])^4 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i
%t 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 *)
%Y Cf. A008292.
%K nonn,tabl
%O 1,2
%A _Olivier Gérard_
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