A374980 Number of multiset permutations of {1, 1, 2, 2, ..., n, n} with no fixed pair (j,j).

1, 0, 5, 74, 2193, 101644, 6840085, 630985830, 76484389121, 11792973495032, 2254432154097861, 523368281765512930, 145044815855963403985, 47302856057098946329284, 17933275902554972391519893, 7820842217155394547769452734, 3887745712142302082441578104705

Offset: 0

Author

Alois P. Heinz, Aug 05 2024

Keywords

• nonn

Comments

Inverse binomial transform of A000680.

Examples

			a(2) = 5: 1212, 1221, 2112, 2121, 2211.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..238

Crossrefs

Cf. A000166, A000459, A000680, A059841, A116218, A375222, A375223.

Column k=2 of A375694.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [1, 0, 5][n+1],
     (n-1)*((2*n+1)*a(n-1)+(4*n-3)*a(n-2)+2*(n-2)*a(n-3)))
    end:
seq(a(n), n=0..16);

Formula

a(n) = Sum_{j=0..n} (-1)^j*binomial(n,j)*A000680(n-j).

a(n) = A116218(n)/2^n.

a(n) mod 2 = 1 - (n mod 2) = A059841(n).