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A239889 From unfriendly seating arrangement problem for fat men at a circular table with n seats.

%I A239889 #18 Jul 29 2018 08:10:23
%S A239889 0,1,2,6,36,216,1440,11520,103824,1032192,11311488,135432000,
%T A239889 1756751040,24546246912,367583014656,5872797874944,99709066195200,
%U A239889 1792707696046080,34026520304848896,679901687704470528,14265989230889290752,313612842057647616000,7208078043054064619520,172883491724308733964288,4319548522560325245210624
%N A239889 From unfriendly seating arrangement problem for fat men at a circular table with n seats.
%H A239889 Philippe Flajolet, <a href="http://algo.inria.fr/libraries/autocomb/fatmen-html/fatmen1.html">A seating arrangement problem</a>. See page 11.
%H A239889 Philippe Flajolet, <a href="/A037256/a037256.pdf">A seating arrangement problem</a> [Cached copy]. See page 11.
%H A239889 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 A239889 gb:=proc(n,b) local k; option remember;
%p A239889 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 A239889 fi
%p A239889 end:
%p A239889 l3:=subs(u=1,diff([seq(gb(j,2),j=0..25)],u));
%p A239889 [seq(l3[i]*(i-1)!,i=1..26)];
%t A239889 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 A239889 D[Table[g[j, 2] j!, {j, 0, 25}], u] /. u -> 1 (* _Jean-François Alcover_, Jul 29 2018, from Maple *)
%Y A239889 Cf. A037256, A239888, A095236.
%K A239889 nonn
%O A239889 0,3
%A A239889 _N. J. A. Sloane_, Mar 29 2014