%I A037223
%S A037223 1,1,2,2,8,8,48,48,384,384,3840,3840,46080,46080,645120,645120,10321920,
%T A037223 10321920,185794560,185794560,3715891200,3715891200,81749606400,
%U A037223 81749606400,1961990553600,1961990553600,51011754393600,51011754393600
%N A037223 Number of solutions to non-attacking rooks problem on n X n board that 
               are invariant under 180 degree rotation.
%C A037223 This is just A000165 doubled up. Normally such sequences do not get their 
               own entry in the OEIS. This is an exception. - N. J. A. Sloane (njas(AT)research.att.com), 
               Sep 23 2006
%C A037223 Also the number of permutations of (1,2,3,...,n) for which the reverse 
               of the inverse is the same as the inverse of the reverse. - Ian Duff 
               (ianfduff(AT)yahoo.co.uk), Mar 09 2007
%D A037223 E. Lucas, Theorie des nombres, Gauthiers-Villars, Paris, 1891, Vol 1, 
               p. 221.
%D A037223 R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial 
               Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).
%H A037223 M. Szabo, <a href="http://www.nexus.hu/mikk/queen/index.html">Non-attacking 
               Queens Problem Page</a>
%F A037223 a(2n) = a(2n+1) = (n)!*2^(n).
%F A037223 Exponential generating function: 1+x+(1+x+x^2)*exp(x^2/2)*sqrt(Pi/2)*erf(x/
               sqrt(2)), where erf denotes the error function. - Antonio G. Astudillo 
               (afg_astudillo(AT)hotmail.com), Nov 01 2002
%F A037223 For asymptotics see the Robinson paper.
%p A037223 For Maple program see A000903.
%Y A037223 Cf. A000165, A033148, A037224, A032522, A037223.
%Y A037223 Sequence in context: A007083 A144060 A016119 this_sequence A066988 A100384 
               A000023
%Y A037223 Adjacent sequences: A037220 A037221 A037222 this_sequence A037224 A037225 
               A037226
%K A037223 nonn
%O A037223 0,3
%A A037223 Miklos SZABO (mike(AT)ludens.elte.hu)
%E A037223 More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), 
               Nov 01 2002
%E A037223 Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2006