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A002136 Matrices with 2 rows.
(Formerly M1668 N0656)
1
1, 2, 6, 23, 109, 618, 4096, 31133, 267219, 2557502, 27011734, 312115953, 3916844779, 53053052462, 771450742596, 11986779006647, 198204672604489, 3475110017769282, 64396888392712366, 1257612452945760503, 25815617698822423341, 555708180579477963962, 12517189538209383465496 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
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
REFERENCES
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).
LINKS
FORMULA
a(n+1) = A002135(n) + n*A002135(n - 1) + n*(n - 1)*a(n - 1). - Joel B. Lewis, Sep 30 2012
a(n) ~ 2^(3/2) * n^(n-2) / exp(n-3/4). - Vaclav Kotesovec, Apr 27 2015
EXAMPLE
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
PROG
(PARI)
/* b(n) := A002135(n) */
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);
/* Joerg Arndt, Apr 07 2013 */
CROSSREFS
Sequence in context: A112501 A093345 A289681 * A328441 A328507 A208733
KEYWORD
nonn
AUTHOR
EXTENSIONS
Added more terms, Joerg Arndt, Apr 07 2013
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)