%I A022558
%S A022558 1,1,2,6,23,103,512,2740,15485,91245,555662,3475090,22214707,144640291,
%T A022558 956560748,6411521056,43478151737,297864793993,2059159989914,
%U A022558 14350039389022,100726680316559,711630547589023,5057282786190872
%N A022558 Number of permutations of length n avoiding the pattern 1342.
%D A022558 Miklos Bona, Exact enumeration of 1342-avoiding permutations; A close 
               link with labeled trees and planar maps, J. Combinatorial Theory, 
               A80 (1997), 257-272.
%D A022558 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 6.48.
%H A022558 M. Bona, <a href="http://arXiv.org/abs/math.CO/9702223">[math/9702223] 
               Exact enumeration of 1342-avoiding permutations: A close link with 
               labeled trees and planar maps</a>
%F A022558 a(n) = (7n^2-3n-2)/2 * (-1)^{n-1} + 3 sum_{i=2,...,n} 2^{i+1} * (2i-4)!/
               {i!(i-2)!} * binomial{n-i+2. 2} * (-1)^{n-i}.
%F A022558 G.f.: 32x/(1+20x-8x^2-(1-8x)^(3/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 13 2004
%e A022558 a(4)=23 because obviously all permutations of length 4 with the exception 
               of 1342 avoid 1342.
%Y A022558 Essentially the same as A004040. Cf. A117158.
%Y A022558 Sequence in context: A098746 A088929 A004040 this_sequence A005802 A061552 
               A053488
%Y A022558 Adjacent sequences: A022555 A022556 A022557 this_sequence A022559 A022560 
               A022561
%K A022558 nonn,easy
%O A022558 0,3
%A A022558 Miklos Bona (bona(AT)math.ufl.edu)
%E A022558 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2004