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Revision History for A002467

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A002467

The game of Mousetrap with n cards (given n letters and n envelopes, how many ways are there to fill the envelopes so that at least one letter goes into its right envelope?).
(history; published version)

#148 by Jon E. Schoenfield at Sat Jan 15 00:24:30 EST 2022

STATUS

editing

approved

#147 by Jon E. Schoenfield at Sat Jan 15 00:24:25 EST 2022

FORMULA

a(n) = - n! * Sum_{i=1..n} (-1)^i/i!. Lim_Limit_{n->infinfinity} a(n)/n! = 1 - 1/e. - Gerald McGarvey, Jun 08 2004

STATUS

approved

editing

#146 by Alois P. Heinz at Wed Sep 01 20:25:36 EDT 2021

STATUS

editing

approved

#145 by Alois P. Heinz at Wed Sep 01 20:25:09 EDT 2021

FORMULA

a(n) = Sum_{k=0..n-1} A047920(n-1,k) for n > 0. - Alois P. Heinz, Sep 01 2021

STATUS

approved

editing

Discussion

Wed Sep 01

20:25

Alois P. Heinz: true for n=0 also ... empty sum gives 0.

#144 by Alois P. Heinz at Wed Sep 01 16:43:28 EDT 2021

STATUS

editing

approved

#143 by Alois P. Heinz at Wed Sep 01 16:40:08 EDT 2021

FORMULA

a(n) = Sum_{k=0..n-1} A047920(n-1,k) for n > 0. - Alois P. Heinz, Sep 01 2021

CROSSREFS

Cf. A002468, A002469, A028306, A047920, A052169, A127899, A276975.

STATUS

approved

editing

#142 by Susanna Cuyler at Wed Jun 24 23:33:01 EDT 2020

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proposed

approved

#141 by Michel Marcus at Wed Jun 24 23:08:54 EDT 2020

STATUS

editing

proposed

#140 by Michel Marcus at Wed Jun 24 23:08:49 EDT 2020

LINKS

Sergi Elizalde, <a href="https://arxiv.org/abs/2006.13842">Bijections for restricted inversion sequences and permutations with fixed points</a>, arXiv:2006.13842 [math.CO], 2020.

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.

STATUS

approved

editing

#139 by Sean A. Irvine at Sat Jun 13 17:51:14 EDT 2020

STATUS

proposed

approved