OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..892
Wikipedia, Permutation.
FORMULA
a(n) mod 2 = A131735(n+3).
a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 - 7/8) * n^(n/2 + 1) / 2^((n+3)/2). - Vaclav Kotesovec, Apr 25 2024
EXAMPLE
a(3) = 2: 123, 321.
a(4) = 4: 1234, 1432, 3214, 4231.
a(5) = 9: 12345, 12543, 14325, 15342, 32145, 32541, 42315, 52143, 52341.
a(6) = 19: 123456, 123654, 125436, 126453, 143256, 143652, 153426, 163254, 163452, 321456, 325416, 326451, 423156, 423651, 521436, 523416, 621453, 623154, 623451.
MAPLE
a:= proc(n) option remember; `if`(n<4, [2$3, 4][n+1],
3*a(n-1)+(n-2)*a(n-2)+(n-1)*(a(n-4)-a(n-3)))/2
end:
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := Sum[Binomial[n - k, k] * Subfactorial[k], {k, 0, n/2}];
Table[a[n], {n, 0, 31}] # Peter Luschny, Apr 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 18 2024
STATUS
approved