A239888 From second moments of unfriendly seating arrangement problem around a circular table with n seats.

0, 0, 0, 8, 48, 464, 4000, 40032, 424704, 4927232, 61553664, 827632640, 11914946560, 183014995968, 2988450177024, 51709354532864, 945292051415040, 18207952013164544, 368620245155184640, 7825923453008609280, 173870718374040305664, 4034781267785209610240, 97622280693411826630656, 2458689656873584082026496, 64361542182239808476151808

Offset: 0

Author

N. J. A. Sloane, Mar 29 2014

Keywords

• nonn

Links

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

Crossrefs

Cf. A037256, A095236, A239889.

Programs

Maple

g:=proc(n) local k; option remember;
if n<=0 then 1 elif n=1 then u else
expand(u/n*convert([seq(g(k-2)*g(n-k-1),k=1..n)],`+`));
fi
end:
l2:=subs(u=1,diff([seq(g(j),j=0..25)],u,u));
[seq(l2[i]*(i-1)!,i=1..26)];

Mathematica

g[n_] := g[n] = Switch[n, -1|0, 1, 1, u, _, u/n Sum[g[k-2] g[n-k-1], {k, 1, n}]];
D[Table[g[j] j!, {j, 0, 25}], {u, 2}] /. u -> 1 (* Jean-François Alcover, Jul 29 2018, from Maple *)