For a string of letters of length k, say abc...def, let f(k) be the string of length k-1 consisting of the adjacent pairs ab, bc, cd, ..., de, ef. Given n, let U be the string of length 2n consisting of n 1's followed by n 2's: 11...122...2. Then a(n) is the number of the C(2n,n) permutations V of U such that f(U) and f(V) agree in exactly one place.

A098813

For a string of letters of length k, say abc...def, let f(k) be the string of length k-1 consisting of the adjacent pairs ab, bc, cd, ..., de, ef. Given n, let U be the string of length 2n consisting of n 1's followed by n 2's: 11...122...2. Then a(n) is the number of the C(2n,n) permutations V of U such that f(U) and f(V) agree in exactly one place.