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%I M2945 N1186 #57 Jun 16 2016 23:27:14
%S 0,0,1,3,13,65,397,2819,22831,207605,2094121,23205383,280224451,
%T 3662810249,51523391965,776082247979,12463259986087,212573743211549,
%U 3837628837381201,73108996989052175,1465703611456618891,30847249002794047793,679998362512214208901,15668677914172813691699,376683592679293811722735
%N The game of Mousetrap with n cards: the number of permutations of n cards having at least one hit after 2.
%C The subsequence of primes begins: 3, 13, 397, 2819, no more through a(19). - _Jonathan Vos Post_, Feb 01 2011
%D 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.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Joerg Arndt, <a href="/A002468/b002468.txt">Table of n, a(n) for n = 1..102</a>
%H R. K. Guy and R. J. Nowakowski, <a href="/A002467/a002467_1.pdf">Mousetrap</a>, Preprint, Feb 10 1993 [Annotated scanned copy]
%H J. Metzger, <a href="/A002467/a002467_3.pdf">Email to N. J. A. Sloane, Apr 30 1991</a>
%H Daniel J. Mundfrom, <a href="http://dx.doi.org/10.1006/eujc.1994.1057">A problem in permutations: the game of 'Mousetrap'</a>. European J. Combin. 15 (1994), no. 6, 555-560.
%H A. Steen, <a href="http://resolver.sub.uni-goettingen.de/purl?PPN600494829_0015/DMDLOG_0031">Some formulas respecting the game of mousetrap</a>, Quart. J. Pure Applied Math., 15 (1878), 230-241.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Mousetrap.html">Mousetrap</a>
%F a(n) = A001563(n) - A002469(n+2). (corrected by _Sean A. Irvine_ and _Joerg Arndt_, Feb 10 2014)
%t a[n_] := (n-2)*(n-2)!-(n-4)*Subfactorial[n-3]-(n-3)*Subfactorial[n-2]; a[1]=a[2]=0; a[3]=1; Table[a[n], {n, 1, 21}] (* _Jean-François Alcover_, Dec 12 2014 *)
%Y Cf. A002467, A002468, A002469, A028306, etc.
%K nonn,easy,nice
%O 1,4
%A _N. J. A. Sloane_
%E Added two more terms, _Joerg Arndt_, Feb 15 2014
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