A007711 Number of unreformed permutations of {1,...,n}.

0, 1, 4, 18, 105, 636, 4710, 38508, 352902, 3563297, 39467081, 475326930, 6198134207, 86912048471, 1305146666727, 20897040866280

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Examples

			For n=3, the 4 unreformed permutations are 123, 231, 312, 213, so a(3)=4. Also 132->123, 321->213 are reformable.
		

References

• A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat n. 15/2005.
• R. K. Guy and R. J. Nowakowski, "Mousetrap," in D. Miklos, V. T. Sos and T. Szonyi, eds., Combinatorics, Paul Erdős is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• A. M. Bersani, On the game Mousetrap.
• A. M. Bersani, Reformed Permutations in mousetrap and its generalizations, INTEGERS, 10 (2010), #G01.
• R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]
• R. K. Guy and R. J. Nowakowski, Mousetrap, Amer. Math. Monthly, 101 (1994), 1007-1010.

Crossrefs

Cf. A007709, A007712, A055459, A067950.

Formula

a(n) = n! - A007709(n). - Sean A. Irvine, Jan 17 2018

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Mar 06 2002

2 more terms from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 07 2007

One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008

a(1) corrected by Joerg Arndt, Dec 24 2014