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

1,3

Comments

The denominator is given by A000254(n).

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.

Links

Table of n, a(n) for n=1..18.

Example

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.

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 *)

Crossrefs

Cf. A093883, A093884, A000254.

Sequence in context: A283779 A353875 A370445 * A192948 A234528 A277300

Adjacent sequences: A093882 A093883 A093884 * A093886 A093887 A093888

Keyword

nonn

Author

Amarnath Murthy, Apr 22 2004

Extensions

More terms from Ryan Propper, Sep 28 2006

Status

approved