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%I #16 Jun 06 2016 22:20:10
%S 0,0,5,60,876,15820,342490,8659697,250596841,8170355939,296392500231,
%T 11842341000706,516766134975841,24454542316972336,1247414741568401188,
%U 68231675778495540368,3983959314088980184276,247324089280835008754847
%N a(n) = floor( {product of all possible sums of (n-1) numbers chosen from among first n numbers} / {sum of all possible products of (n-1) numbers chosen from among first n numbers} ).
%C The denominator is given by A000254(n).
%D Amarnath Murthy, Another combinatorial approach towards generalizing the AM GM inequality, Octogon Mathematical Magazine Vol. 8, No. 2, October 2000.
%D Amarnath Murthy, Smarandache Dual Symmetric Functions And Corresponding Numbers Of The Type Of Stirling Numbers Of The First Kind. Smarandache Notions Journal Vol. 11, No. 1-2-3 Spring 2000.
%e a(1) = 1, a(2) = floor((1*2)/(1+2)) = 1, a(3) = floor((1+2)*(1+3)*(2+3)/(1*2+1*3+2*3)) = floor(60/11) = 5.
%t Do[l = Select[Subsets[Range[n]], Length[ # ]==n-1&]; a = Times @@ Map[Plus @@ #&, l]; b = Plus @@ Map[Times @@ #&, l]; Print[Floor[a/b]], {n, 1, 20}] (* _Ryan Propper_, Sep 28 2006 *)
%Y Cf. A093883, A093884, A000254.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Apr 22 2004
%E More terms from _Ryan Propper_, Sep 28 2006