A258216 Number of permutations of {1,2,3,...,n} such that no multiples of 3 are adjacent.
1, 1, 2, 6, 24, 120, 480, 3600, 30240, 151200, 1693440, 20321280, 121927680, 1828915200, 28740096000, 201180672000, 3793692672000, 73977007104000, 591816056832000, 13463815292928000, 314155690168320000
Offset: 0
Programs
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Mathematica
Table[Factorial[n-Floor[n/3]]*FactorialPower[n+1-Floor[n/3],Floor[n/3],1], {n, 0, 20}]
Formula
a(n) = factorial(n-floor(n/3))*fallfac(n+1-floor(n/3),floor(n/3)), where fallfac is falling factorial, A008279.
a(n) ~ n! * 2^(2*n+2-2*floor(n,3)/3) / 3^(n+1/2). - Vaclav Kotesovec, May 23 2015