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A114938 Number of permutations of the multiset {1,1,2,2,....,n,n} with no two consecutive terms equal. 9
0, 2, 30, 864, 39480, 2631600, 241133760, 29083420800, 4467125013120, 851371260364800, 197158144895712000, 54528028997584665600, 17752366094818747392000, 6720318485119046923315200, 2927066537906697348594432000, 1453437879238150456164433920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is also the number of $(0,1)$~- matrices $A=(a_{ij})$ of size $n\times (2n)$ such that each row has exactly two $1$'s and each column has exactly one $1$'s and with the restriction that no $1$ stands on the line from $a_{11}$ to $% a_{22}$ . [From Shanzhen Gao, Feb 24 2010]

REFERENCES

R. P. Stanley, Enumerative Combinatorics Volume I, Cambridge University Press, 1997. Chapter 2, Sieve Methods, Example 2.2.3, page 68.

Shanzhen Gao, Sequences Arising from Integer Matrix Enumeration (in preparation) [From Shanzhen Gao, Feb 24 2010]

LINKS

Andrew Woods, Table of n, a(n) for n = 1..100

FORMULA

a(n) = Sum_{k=0..n} ((C(n, k)*(-1)^(n-k)*(n+k)!)/2^k).

a(n) = (-1)^n * n! * A000806(n), n>0. [Vladeta Jovovic, Nov 19 2009]

a(n) = n*(2*n-1)*a(n-1) + (n-1)*n*a(n-2). - Vaclav Kotesovec, Aug 07 2013

a(n) ~ 2^(n+1)*n^(2*n)*sqrt(Pi*n)/exp(2*n+1). - Vaclav Kotesovec, Aug 07 2013

EXAMPLE

a(2) = 2 because there are two permutations of {1,1,2,2} avoiding equal consecutive terms: 1212 and 2121.

MATHEMATICA

Table[Sum[Binomial[n, i](2n-i)!/2^(n-i) (-1)^i, {i, 0, n}], {n, 20}]  (* Geoffrey Critzer, Jan 02 2013 *)

CROSSREFS

Cf. A114939 = preferred seating arrangements of n couples.

Cf. A007060 = arrangements of n couples with no adjacent spouses; A007060(n) = 2^n * A114938(n) (this sequence).

Sequence in context: A160694 A013525 A229781 * A082653 A186292 A140174

Adjacent sequences:  A114935 A114936 A114937 * A114939 A114940 A114941

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 08 2006

STATUS

approved

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Last modified April 16 12:16 EDT 2014. Contains 240591 sequences.