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A114938 Number of permutations of the multiset {1,1,2,2,....,n,n} with no two consecutive terms equal. 12
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 X 2n such that each row has exactly two 1's and each column has exactly one 1 and with the restriction that no 1 stands on the line from a_11 to a_22. - 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.

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} ((binomial(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 *)

PROG

(PARI) vector(20, n, sum(k=0, n, binomial(n, k)*(-1)^(n-k)*(n+k)!/2^k)) \\ Michel Marcus, Aug 10 2015

(MAGMA) I:=[0, 2]; [n le 2 select I[n] else n*(2*n-1)*Self(n-1) + (n-1)*n*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Aug 10 2015

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: A013525 A270531 A229781 * A082653 A274389 A186292

Adjacent sequences:  A114935 A114936 A114937 * A114939 A114940 A114941

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 08 2006

STATUS

approved

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Last modified December 10 19:28 EST 2016. Contains 279006 sequences.