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 A000279 Card matching: coefficients B[n,1] of t in the reduced hit polynomial A[n,n,n](t). (Formerly M3106 N1258) 4
 3, 24, 216, 1824, 15150, 124416, 1014888, 8241792, 66724398, 538990800, 4346692680, 35009591040, 281699380560, 2264868936960, 18198009147600, 146142982814208, 1173123636533454, 9413509300965936, 75513633110271264, 605598295606296000, 4855626127979443908, 38924245740546950784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 FORMULA 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) = n^2*(A000172(n)+4*A000172(n-1))/(n+1). - Mark van Hoeij, Oct 26 2011 a(n) ~ 8^n*sqrt(3)/Pi = 8^n*0.5513... - M. F. Hasler, Sep 21 2015 a(n) = 3n*A262407(n). - M. F. Hasler, Sep 23 2015 MATHEMATICA f[n_] := HypergeometricPFQ[{-n, -n, -n}, {1, 1}, -1]; a[n_] := n^2*(f[n]+4*f[n-1])/(n+1); Array[a, 20] (* Jean-François Alcover, Mar 11 2014, after Mark van Hoeij *) PROG (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 CROSSREFS Cf. A000489, A000535. Cf. A033581. Sequence in context: A073978 A278991 A232692 * A292311 A279973 A274737 Adjacent sequences:  A000276 A000277 A000278 * A000280 A000281 A000282 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Apr 26 2000 More terms from Emeric Deutsch, Feb 19 2004 Three lines of data completed and more explicit definition by M. F. Hasler, Sep 21 2015 STATUS approved

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Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)