Partition first N integers into fractions with an integer sum

[Max Alekseyev]

On Wed, May 14, 2008 at 1:43 AM, Max Alekseyev <maxale at gmail.com> wrote:
> On Tue, May 13, 2008 at 12:12 PM, Jack Brennen <jb at brennen.net> wrote:
>
>> Take the first 2*N integers and using each integer once and only
>> once as either a numerator or a denominator, construct N fractions
>> whose sum is an integer.
>>
>> How many unique solutions are there for each N?
>>
>> The sequence seems to begin:  1,1,7,21,190,...
>
> Here are a couple of further values:
> 1, 1, 7, 21, 190, 1007, 6972,

and one more:
1, 1, 7, 21, 190, 1007, 6972, 111554,

Regards,
Max