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%I #9 Mar 05 2013 09:12:25
%S 1,7,1,163,52,1,8873,4719,231,1,930581,731646,64966,806,1,166430695,
%T 180969681,25235006,610166,2451,1,46667364787,67248150516,13560308427,
%U 543687292,4546137,6840,1,19297882224241,35761409868799,9882496297869
%N Cube of the lower triangular normalized Eulerian number matrix.
%F Numerators of lower triangle of (a[ i, j ])^3 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i
%t 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 *)
%Y Cf. A008292.
%K nonn,tabl
%O 1,2
%A _Olivier Gérard_
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