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Take the first 2n integers and using each integer once and only once as either a numerator or a denominator, construct n fractions whose sum is an integer; a(n) = number of distinct solutions for n.
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%I #18 Oct 29 2022 04:34:09

%S 1,1,7,21,190,1007,6972,111554,1040635

%N Take the first 2n integers and using each integer once and only once as either a numerator or a denominator, construct n fractions whose sum is an integer; a(n) = number of distinct solutions for n.

%C The old entry with this sequence number was a duplicate of A048298.

%o (PARI) { npairs(n) = loca(r,q,z); r=0;

%o forvec(p=vector(n,i,[1,2*n]),

%o q = eval( setminus( Set(vector(2*n,i,i)), Set(p) ) );

%o for(j=1,n!,

%o z=numtoperm(n,j);

%o if(type( sum(j=1,#p,p[j]/q[z[j]]) )=="t_INT",r++); );, 2); r }

%o /* _Max Alekseyev_, May 14 2008 */

%K nonn

%O 1,3

%A _Jack Brennen_, May 13 2008

%E a(6)-a(8) from _Max Alekseyev_, May 14 2008

%E Edited by _Charles R Greathouse IV_, Oct 28 2009

%E a(9) from _Sean A. Irvine_, Oct 29 2022