cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A239888 #22 Jul 29 2018 08:10:16
%S A239888 0,0,0,8,48,464,4000,40032,424704,4927232,61553664,827632640,
%T A239888 11914946560,183014995968,2988450177024,51709354532864,
%U A239888 945292051415040,18207952013164544,368620245155184640,7825923453008609280,173870718374040305664,4034781267785209610240,97622280693411826630656,2458689656873584082026496,64361542182239808476151808
%N A239888 From second moments of unfriendly seating arrangement problem around a circular table with n seats.
%H A239888 Philippe Flajolet, <a href="http://algo.inria.fr/libraries/autocomb/fatmen-html/fatmen1.html">A seating arrangement problem</a>
%H A239888 Philippe Flajolet, <a href="/A037256/a037256.pdf">A seating arrangement problem</a> [Cached copy]
%H A239888 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 A239888 g:=proc(n) local k; option remember;
%p A239888 if n<=0 then 1 elif n=1 then u else
%p A239888 expand(u/n*convert([seq(g(k-2)*g(n-k-1),k=1..n)],`+`));
%p A239888 fi
%p A239888 end:
%p A239888 l2:=subs(u=1,diff([seq(g(j),j=0..25)],u,u));
%p A239888 [seq(l2[i]*(i-1)!,i=1..26)];
%t A239888 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 A239888 D[Table[g[j] j!, {j, 0, 25}], {u, 2}] /. u -> 1 (* _Jean-François Alcover_, Jul 29 2018, from Maple *)
%Y A239888 Cf. A037256, A095236, A239889.
%K A239888 nonn
%O A239888 0,4
%A A239888 _N. J. A. Sloane_, Mar 29 2014