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%I M4507 N1908 #34 May 09 2020 15:12:15
%S 2,0,0,8,30,192,1344,10800,97434,976000,10749024,129103992,1679495350,
%T 23525384064,353028802560,5650370001120,96082828074162,
%U 1729886440780800,32874134679574208,657589108734075240,13811277748363437006,303884178002526338624
%N Coefficients of ménage hit polynomials.
%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%F 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
%F 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
%F Conjecture: a(n) = 2*n*A000271(n). - _R. J. Mathar_, Nov 02 2015
%t 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 *)
%Y A diagonal of A058087. Cf. A000179.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Simon Plouffe_
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