login
A374980
Number of multiset permutations of {1, 1, 2, 2, ..., n, n} with no fixed pair (j,j).
7
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 05 2024
STATUS
approved