OFFSET
0,3
COMMENTS
Arises from "Unfriendly Seating Arrangement" problem around a circular table.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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.
FORMULA
E.g.f.: (1-exp(-2*x))*(1-x)^(-2)/2.
a(n) = 2*(n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 08 2012
a(n) ~ (1-1/e^2)*n!*n/2. - Vaclav Kotesovec, Oct 08 2012
a(n) = (-2)^n + (n+1)!/2 - (3+n)*Gamma(1+n,-2)/(2*e^2). - Benedict W. J. Irwin, Jul 06 2020
MAPLE
f:=n->n!*add((n-i)*(-2)^i/(i+1)!, i=0..n-1);
[seq(f(n), n=0..50)]; # N. J. A. Sloane, Mar 29 2014
MATHEMATICA
m = 19; CoefficientList[ Series[(1 - Exp[-2x])*(1/((1-x)^2*2)), {x, 0, m}], x]*Range[0, m]!
(* Jean-François Alcover, Jun 28 2011 *)
Flatten[{0, Table[n!*Sum[Sum[(-1)^j*2^j/(j+1)!, {j, 0, k}], {k, 0, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 27 2012 *)
PROG
(PARI) x='x+O('x^66); concat([0], Vec(serlaplace((1-exp(-2*x))/(2*(1-x)^2)))) \\ Joerg Arndt, May 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Mar 29 2014
STATUS
approved