A026013 a(n) = number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2n) = 4. Also a(n) = T(2n,n-1), where T is the array defined in A026009.

1, 4, 15, 55, 200, 726, 2639, 9620, 35190, 129200, 476102, 1760673, 6533150, 24319050, 90795375, 339929880, 1275977670, 4801199400, 18106714050, 68430306750, 259129680264, 983085703116, 3736124441990, 14222020085880, 54221213973500