Number of permutations of the numbers 1 through 2n satisfying the "Alex Fink" condition: there is one and only one partial sum in each interval (k(n+1),(k+1)(n+1)] for 0<=k<2n-1.

a(2)=8 since there are eight permutations of (1,2,3,4) satisfying the Fink condition: (1,3,4,2), (1,4,2,3), (1,4,3,2), (2,4,1,3) and their mirror images.