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 A114938 Number of permutations of the multiset {1,1,2,2,...,n,n} with no two consecutive terms equal. 15
 1, 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 0,3 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 a(n) is the number of permutations of the multiset {1,1,2,2,...,n,n} with no fixed points. - Alexander Burstein, May 16 2020 REFERENCES R. P. Stanley, Enumerative Combinatorics Volume I, Cambridge University Press, 1997. Chapter 2, Sieve Methods, Example 2.2.3, page 68. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..238 (terms 1..100 from Andrew Woods) H. Eriksson, A. Martin, Enumeration of Carlitz multipermutations, arXiv:1702.04177 [math.CO], 2017. 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 a(n) = n! * A278990(n). - Alexander Burstein, May 16 2020 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, 0, 20}]  (* Geoffrey Critzer, Jan 02 2013, and adapted to the extension by Stefano Spezia, Nov 15 2018 *) 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). Cf. A193638. Cf. A278990 = number of loopless linear chord diagrams with n chords. Cf. A000806 = Bessel polynomial y_n(-1). Sequence in context: A013525 A270531 A229781 * A082653 A332231 A274389 Adjacent sequences:  A114935 A114936 A114937 * A114939 A114940 A114941 KEYWORD nonn AUTHOR Hugo Pfoertner, Jan 08 2006 EXTENSIONS a(0)=1 prepended by Seiichi Manyama, Nov 15 2018 STATUS approved

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Last modified July 6 08:51 EDT 2020. Contains 335476 sequences. (Running on oeis4.)