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A000425
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Coefficients of ménage hit polynomials.
(Formerly M4507 N1908)
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8
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2, 0, 0, 8, 30, 192, 1344, 10800, 97434, 976000, 10749024, 129103992, 1679495350, 23525384064, 353028802560, 5650370001120, 96082828074162, 1729886440780800, 32874134679574208, 657589108734075240, 13811277748363437006, 303884178002526338624
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OFFSET
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1,1
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.
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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Table of n, a(n) for n=1..22.
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FORMULA
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It appears that a(n) = round(4*n*exp(-2)*(BesselK(n-1,2)+BesselK(n,2))) when n >= 10. - Mark van Hoeij, Oct 25 2011
Conjecture: (n-1)*(n-3)*a(n) -n*(n-2)*(n-3)*a(n-1) -n*(n-1)*(n-3)*a(n-2) -n *(n-1)*a(n-3)=0. - R. J. Mathar, Nov 02 2015
Conjecture: a(n) = 2*n*A000271(n). - R. J. Mathar, Nov 02 2015
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MATHEMATICA
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p[n_] := Sum[2*n/(2*n-k)*Binomial[2*n-k, k]*(n-k)!*(x-1)^k, {k, 0, n}] // CoefficientList[#, x]&; Array[p, 25][[All, 2]] (* Jean-François Alcover, Feb 08 2016 *)
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CROSSREFS
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A diagonal of A058087. Cf. A000179.
Sequence in context: A236925 A134414 A113036 * A230878 A349369 A349352
Adjacent sequences: A000422 A000423 A000424 * A000426 A000427 A000428
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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