A381759 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 does not exceed the last.

1, 1, 3, 5, 11, 38, 182, 938, 4158, 23384, 160104, 1063772, 6987380, 53746000, 479965824, 4182552416, 35963592624, 351432650816, 3860219984448, 41614300175968

Offset

1,3

Links

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

Chinese BBS for the problem

Formula

a(n) = A381760(n) + A176127(n).

Example

a(4) = 5 since there are 5 different solutions: 131423024, 141302432, 240231413, 023421314, 041312432.

Crossrefs

Cf. A014552, A176127, A381760.

Sequence in context: A254402 A060881 A035345 * A254401 A174915 A162250

Adjacent sequences: A381756 A381757 A381758 * A381760 A381761 A381762

Keyword

nonn,more

Author

Zhao Hui Du, Mar 06 2025

Status

approved