%I A033815
%S A033815 1,1,14,426,24024,2170680,287250480,52370755920,12585067447680,
%T A033815 3854801333416320,1465957162768492800,677696237345719468800,
%U A033815 374281829360322587827200,243388909697235614324812800,184070135024053703140543027200
%N A033815 Number of standard permutations of [ a_1..a_n b_1..b_n ] (b_i is not 
               immediately followed by a_i, for all i).
%C A033815 Also turns up as the solution to Problem #18, p. 326 of Alan Tucker's 
               Applied Combinatorics, 4th ed, Wiley NY 2002 [Tucker's `n' is the 
               `2n' here]. - John L Leonard, Sep 15 2003
%D A033815 Leo Chao, Paul DesJarlais and John L Leonard, A binomial identity, via 
               derangements, Math. Gaz. 89 (2005), 268-270..
%D A033815 R. P. Stanley, Enumerative Combinatorics I, Chap.2, Exercise 10, p. 89.
%H A033815 Ira Gessel, <a href="http://www.mat.univie.ac.at/~slc/opapers/s17gessel.html">
               Enumerative applications of symmetric functions</a>
%F A033815 a(n)=2n(2n-1)a(n-1)+n(n-1)a(n-2); a(n)=sum(binomial(n, i)*(-1)^i*(2*n-i)!, 
               i=0..n).
%F A033815 a(n) = sum_{i=0}^n [ {nchoose i} (2n-i)! sum_{j=0}^{2n-i} (-1)^j/j! ]; 
               also a(n) = n! sum_{i=0}^n {nchoose i} n!/(n-i)! [ sum_{j=0}^{n-i} 
               (-1)^j {n-i choose j} (n-j)!/i! ]. - John L Leonard, Sep 15 2003
%F A033815 a(n) = Sum_{k=0..n} binomial(n,k)*A000166(n+k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 04 2006
%p A033815 A033815 := proc(n) local i; add(binomial(n, i)*(-1)^i*(2*n - i)!, i = 
               0 .. n) end;
%Y A033815 A002119[ n ]*n!.
%Y A033815 Main diagonal of array in A068106.
%Y A033815 Sequence in context: A097310 A041367 A041364 this_sequence A103916 A005790 
               A128051
%Y A033815 Adjacent sequences: A033812 A033813 A033814 this_sequence A033816 A033817 
               A033818
%K A033815 nonn,easy,nice
%O A033815 0,3
%A A033815 N. J. A. Sloane (njas(AT)research.att.com).