A060146 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.

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

Offset: 1

Author

Jack Brennen, May 13 2008

Keywords

• nonn

Comments

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

Programs

PARI

{ npairs(n) = loca(r,q,z); r=0;
forvec(p=vector(n,i,[1,2*n]),
q = eval( setminus( Set(vector(2*n,i,i)), Set(p) ) );
for(j=1,n!,
z=numtoperm(n,j);
if(type( sum(j=1,#p,p[j]/q[z[j]]) )=="t_INT",r++); );, 2); r }
/* Max Alekseyev, May 14 2008 */

Extensions

a(6)-a(8) from Max Alekseyev, May 14 2008

Edited by Charles R Greathouse IV, Oct 28 2009

a(9) from Sean A. Irvine, Oct 29 2022