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%I #9 Mar 05 2013 09:12:35
%S 1,3,1,19,16,1,201,319,55,1,3131,8296,2816,156,1,66883,274089,158774,
%T 18254,399,1,1866103,11233692,10137723,2064028,99093,960,1,65599089,
%U 559402687,738815949,240080355,21320275,481821,2223,1,2826880471
%N Square of the lower triangular normalized Eulerian number matrix.
%F Numerators of lower triangle of (a[ i, j ])^2 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i
%t rows = 9; 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}]; m2 = m.m; Table[fracs = m2[[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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