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A002136
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Matrices with 2 rows.
(Formerly M1668 N0656)
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1
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1, 2, 6, 23, 109, 618, 4096, 31133, 267219, 2557502, 27011734, 312115953, 3916844779, 53053052462, 771450742596, 11986779006647, 198204672604489, 3475110017769282, 64396888392712366, 1257612452945760503, 25815617698822423341, 555708180579477963962, 12517189538209383465496
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OFFSET
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3,2
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COMMENTS
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a(n) is the number of ways in which a deck with n - 1 matched pairs and two singleton cards may be dealt into n hands of two cards, assuming the order of the hands and the order of the cards in each hand is irrelevant. (See Art of Problem Solving link for proof.) - Joel B. Lewis, Sep 30 2012
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REFERENCES
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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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FORMULA
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EXAMPLE
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For n = 3, the a(3) = 6 ways to partition the deck {1, 1, 2, 2, 3, 4} into three pairs are {11, 22, 34}, {12, 12, 34}, {13, 14, 22}, {11, 23, 24}, {12, 13, 24} and {12, 14, 23}. - Joel B. Lewis, Sep 30 2012
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PROG
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(PARI)
b(n) = if(n<3, [1, 1, 2][n+1], n*b(n-1) - (n-1)*(n-2)*b(n-3)/2 );
c(n) = if(n<3, [1, 2][n], b(n-1) + (n-1)*b(n-2) + (n-1)*(n-2)*c(n-2) );
a(n) = c(n-2);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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