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

0, 1, 2, 6, 36, 216, 1440, 11520, 103824, 1032192, 11311488, 135432000, 1756751040, 24546246912, 367583014656, 5872797874944, 99709066195200, 1792707696046080, 34026520304848896, 679901687704470528, 14265989230889290752, 313612842057647616000, 7208078043054064619520, 172883491724308733964288, 4319548522560325245210624

Offset: 0

Author

N. J. A. Sloane, Mar 29 2014

Keywords

• nonn

Links

• Philippe Flajolet, A seating arrangement problem. See page 11.
• Philippe Flajolet, A seating arrangement problem [Cached copy]. See page 11.
• Dave Freedman and Larry Shepp, An unfriendly seating arrangement, Problem 62-3, SIAM Review, Vol. 6 (1964), 180-182.

Crossrefs

Cf. A037256, A239888, A095236.

Programs

Maple

gb:=proc(n,b) local k; option remember;
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)],`+`))
fi
end:
l3:=subs(u=1,diff([seq(gb(j,2),j=0..25)],u));
[seq(l3[i]*(i-1)!,i=1..26)];

Mathematica

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