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

1,4

Links

Table of n, a(n) for n=1..20.

Chinese BBS for the problem

Formula

a(n) = A381759(n) - A176127(n).

Example

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.

Crossrefs

Cf. A014552, A176127, A381759.

Sequence in context: A273526 A026943 A307571 * A391408 A384705 A047096

Adjacent sequences: A381757 A381758 A381759 * A381761 A381762 A381763

Keyword

nonn,more

Author

Zhao Hui Du, Mar 06 2025

Status

approved