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A000279
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Card matching: coefficients B[n,1] of t in the reduced hit polynomial A[n,n,n](t).
(Formerly M3106 N1258)
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4
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3, 24, 216, 1824, 15150, 124416, 1014888, 8241792, 66724398, 538990800, 4346692680, 35009591040, 281699380560, 2264868936960, 18198009147600, 146142982814208, 1173123636533454, 9413509300965936, 75513633110271264, 605598295606296000, 4855626127979443908, 38924245740546950784
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OFFSET
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1,1
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COMMENTS
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Number of permutations of 3 distinct letters (ABC) each with n copies such that one (1) fixed points. E.g., if AAAAABBBBBCCCCC n=3*5 letters permutations then one fixed points n5=15150. - Zerinvary Lajos, Feb 02 2006
The definition uses notations of Riordan (1958), except for use of n instead of p. - M. F. Hasler, Sep 22 2015
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 193.
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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a(n) = 3n * sum(C(n, k+1)*C(n, k)*C(n-1, k), k=0..n-1).
G.f.: x * (6*hypergeom([4/3, 5/3],[2],27*x^2/(1-2*x)^3)/(1-2*x)^3 - 3*hypergeom([2/3, 4/3],[1],27*x^2/(1-2*x)^3)/(1-2*x)^2). - Mark van Hoeij, Oct 23 2011
a(n) ~ 8^n*sqrt(3)/Pi = 8^n*0.5513... - M. F. Hasler, Sep 21 2015
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MATHEMATICA
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PROG
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(PARI) A000279(n)=3*n*sum(k=0, n-1, binomial(n, k+1)*binomial(n, k)*binomial(n-1, k)) \\ M. F. Hasler, Sep 21 2015
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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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Three lines of data completed and more explicit definition by M. F. Hasler, Sep 21 2015
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STATUS
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approved
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