A026031 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) = 3, s(2n) = 7. Also a(n) = T(2n,n-2), where T is defined in A026022.

1, 6, 28, 120, 494, 1988, 7888, 31008, 121125, 471086, 1826660, 7068360, 27313650, 105452700, 406923360, 1569869760, 6056194410, 23366193084, 90173331960, 348102883184, 1344324544156, 5193831553416, 20075820280544, 77637309982400