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%I #8 Mar 05 2013 08:24:23
%S 1,15,1,4383,609,8,332945,70127,1920,8,3818466833,1071459023,45021783,
%T 392486,675,117707753216845145,41103397063050887,2332341110766495,
%U 31497752932598,113377876875,94910400,28982153439665068102728041
%N 4th power of the lower triangular normalized 2nd kind Stirling matrix.
%F Numerators of lower triangle of (a[ i, j ])^4 where a[ i, j ] = S(i, j)/BellNumber(i) if j<=i, 0 if j>i
%t rows = 7; m = Table[If[k <= n, StirlingS2[n, k]/BellB[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. A008277.
%K nonn,tabl
%O 1,2
%A _Olivier Gérard_