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

0,3

Comments

Inverse binomial transform of A000680.

Links

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

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).

Example

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

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);

Crossrefs

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

Column k=2 of A375694.

Sequence in context: A126740 A251666 A192564 * A080473 A266570 A355121

Adjacent sequences: A374977 A374978 A374979 * A374981 A374982 A374983

Keyword

nonn

Author

Alois P. Heinz, Aug 05 2024

Status

approved