A258213 Number of permutations of {1,2,3,...,n} such that no even numbers are adjacent.

1, 1, 2, 6, 12, 72, 144, 1440, 2880, 43200, 86400, 1814400, 3628800, 101606400, 203212800, 7315660800, 14631321600, 658409472000, 1316818944000, 72425041920000, 144850083840000, 9560105533440000, 19120211066880000, 1491376463216640000, 2982752926433280000

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = factorial(ceiling(n/2))*fallfac(ceiling(n/2)+1, floor(n/2)), with fallfac = A008279.

a(2n) = A010790(n), a(2n-1) = A010790(n)/2.

D-finite with recurrence: (4*(n-2)^2 + 24*n - 80)*a(n) + (16*n+24)*a(n-1) - (n+2)*n*((n-2)^2 + 8*n - 17)*a(n-2) = 0. - Georg Fischer, Nov 23 2022

Maple

a:= n-> (m-> m!^2*(m+1))(iquo(n+1, 2, 'r'))/(2-r):
seq(a(n), n=0..24);  # Alois P. Heinz, Feb 14 2024

Prog

(PARI) T(n, k) = n!/(n-k)!; \\ A008279
a(n) = ceil(n/2)!*T(ceil(n/2)+1, n\2); \\ Michel Marcus, Nov 24 2022

Crossrefs

Cf. A008279, A010790.

Sequence in context: A090747 A287142 A076220 * A178846 A173843 A107763

Adjacent sequences: A258210 A258211 A258212 * A258214 A258215 A258216

Keyword

nonn

Author

Ran Pan, May 23 2015

Status

approved