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%I #8 Mar 05 2013 08:24:30
%S 1,3,1,27,21,2,173,227,48,2,2213,4283,1479,134,3,1239065,3303383,
%T 1635807,238718,11475,156,1178661599,4156965497,2749126434,569141150,
%U 43679400,1263600,11310,537440137205,2439821215787,2061668165820
%N Square of lower triangular normalized 2nd kind Stirling matrix.
%F Numerators of lower triangle of (a[ i, j ])^2 where a[ i, j ] = S(i, j)/BellNumber(i) if j<=i, 0 if j>i
%t rows = 8; m = Table[If[k <= n, StirlingS2[n, k]/BellB[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. A008277.
%K nonn,tabl
%O 1,2
%A _Olivier Gérard_
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