A093885 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} ).

0, 0, 5, 60, 876, 15820, 342490, 8659697, 250596841, 8170355939, 296392500231, 11842341000706, 516766134975841, 24454542316972336, 1247414741568401188, 68231675778495540368, 3983959314088980184276, 247324089280835008754847

Offset: 1

Author

Amarnath Murthy, Apr 22 2004

Keywords

• nonn

Comments

The denominator is given by A000254(n).

Examples

			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.
		

References

• Amarnath Murthy, Another combinatorial approach towards generalizing the AM-GM inequality, Octogon Mathematical Magazine Vol. 8, No. 2, October 2000.
• 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.

Crossrefs

Cf. A093883, A093884, A000254.

Programs

Mathematica

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 *)

Extensions

More terms from Ryan Propper, Sep 28 2006