A239888 - OEIS

%I #22 Jul 29 2018 08:10:16

%S 0,0,0,8,48,464,4000,40032,424704,4927232,61553664,827632640,

%T 11914946560,183014995968,2988450177024,51709354532864,

%U 945292051415040,18207952013164544,368620245155184640,7825923453008609280,173870718374040305664,4034781267785209610240,97622280693411826630656,2458689656873584082026496,64361542182239808476151808

%N From second moments of unfriendly seating arrangement problem around a circular table with n seats.

%H Philippe Flajolet, <a href="http://algo.inria.fr/libraries/autocomb/fatmen-html/fatmen1.html">A seating arrangement problem</a>

%H Philippe Flajolet, <a href="/A037256/a037256.pdf">A seating arrangement problem</a> [Cached copy]

%H Dave Freedman and Larry Shepp, <a href="http://dx.doi.org/10.1137/1004037">An unfriendly seating arrangement, Problem 62-3</a>, SIAM Review, Vol. 6 (1964), 180-182.

%p g:=proc(n) local k; option remember;

%p if n<=0 then 1 elif n=1 then u else

%p expand(u/n*convert([seq(g(k-2)*g(n-k-1),k=1..n)],`+`));

%p fi

%p end:

%p l2:=subs(u=1,diff([seq(g(j),j=0..25)],u,u));

%p [seq(l2[i]*(i-1)!,i=1..26)];

%t g[n_] := g[n] = Switch[n, -1|0, 1, 1, u, _, u/n Sum[g[k-2] g[n-k-1], {k, 1, n}]];

%t D[Table[g[j] j!, {j, 0, 25}], {u, 2}] /. u -> 1 (* _Jean-François Alcover_, Jul 29 2018, from Maple *)

%Y Cf. A037256, A095236, A239889.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Mar 29 2014