A381760 Number of words of length 2n+1 with one 0 entry and two entries of each of 1..n so that there are exactly k numbers between two equal k's and so that the first element is not 0 and also does not exceed the last.
1, 1, 1, 3, 11, 38, 130, 638, 4158, 23384, 124520, 847484, 6987380, 53746000, 400346544, 3529108816, 35963592624, 351432650816, 3346590201888, 36341624453568
Offset: 1
Examples
For n=4, there are 3 different ways {131423024, 141302432, 240231413} so that a(4)=3 and both 023421314 and 041312432 are invalid since 0 in boundary.