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A002468
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The game of Mousetrap with n cards: the number of permutations of n cards having at least one hit after 2.
(Formerly M2945 N1186)
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8
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0, 0, 1, 3, 13, 65, 397, 2819, 22831, 207605, 2094121, 23205383, 280224451, 3662810249, 51523391965, 776082247979, 12463259986087, 212573743211549, 3837628837381201, 73108996989052175, 1465703611456618891, 30847249002794047793, 679998362512214208901, 15668677914172813691699, 376683592679293811722735
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OFFSET
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1,4
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COMMENTS
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The subsequence of primes begins: 3, 13, 397, 2819, no more through a(19). - Jonathan Vos Post, Feb 01 2011
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REFERENCES
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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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]
Eric Weisstein's World of Mathematics, Mousetrap
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FORMULA
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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