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 A000425 Coefficients of ménage hit polynomials. (Formerly M4507 N1908) 8
 2, 0, 0, 8, 30, 192, 1344, 10800, 97434, 976000, 10749024, 129103992, 1679495350, 23525384064, 353028802560, 5650370001120, 96082828074162, 1729886440780800, 32874134679574208, 657589108734075240, 13811277748363437006, 303884178002526338624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES 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). LINKS FORMULA 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 MATHEMATICA 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 *) CROSSREFS A diagonal of A058087. Cf. A000179. Sequence in context: A236925 A134414 A113036 * A230878 A349369 A349352 Adjacent sequences: A000422 A000423 A000424 * A000426 A000427 A000428 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)