A239889 - OEIS

%I #18 Jul 29 2018 08:10:23

%S 0,1,2,6,36,216,1440,11520,103824,1032192,11311488,135432000,

%T 1756751040,24546246912,367583014656,5872797874944,99709066195200,

%U 1792707696046080,34026520304848896,679901687704470528,14265989230889290752,313612842057647616000,7208078043054064619520,172883491724308733964288,4319548522560325245210624

%N From unfriendly seating arrangement problem for fat men at 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>. See page 11.

%H Philippe Flajolet, <a href="/A037256/a037256.pdf">A seating arrangement problem</a> [Cached copy]. See page 11.

%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 gb:=proc(n,b) local k; option remember;

%p if n<=0 then 1 elif n<=b then u else expand(u/n*convert([seq(gb(k-b-1,b)*gb(n-k-b,b),k=1..n)],`+`))

%p fi

%p end:

%p l3:=subs(u=1,diff([seq(gb(j,2),j=0..25)],u));

%p [seq(l3[i]*(i-1)!,i=1..26)];

%t g[n_, b_] := g[n, b] = Which[n <= 0, 1, n <= b, u, True, u/n Sum[g[k-b-1, b] g[n-k-b, b], {k, 1, n}]];

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

%Y Cf. A037256, A239888, A095236.

%K nonn

%O 0,3

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