Search: id:A056986
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%I A056986
%S A056986 0,0,1,10,78,588,4611,38890,358018,3612004,39858014,478793588,
%T A056986 6226277900,87175616760,1307664673155,20922754530330,355687298451210,
%U A056986 6402373228089300,121645098641568810,2432902001612519580
%N A056986 Number of permutations on {1,...,n} containing any given pattern alpha 
               in the symmetric group S_3.
%C A056986 This is well-defined because for all patterns alpha in S_3 the number 
               of permutations in S_n avoiding alpha is the same (the Catalan numbers). 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2008
%D A056986 R. Simion and F.W. Schmidt, Restricted Permutations, Europ. J. Comb., 
               6, 1985, 383-406.
%H A056986 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PermutationPattern.html">Link to a section of The World of Mathematics.</
               a>
%e A056986 a(4)=10 because, taking, for example, the pattern alpha=321, we have 
               3214, 3241, 1432, 2431, 3421, 4213, 4132, 4231, 4312 and 4321.
%t A056986 n!-Binomial[2n, n]/(n+1)
%Y A056986 Sequence in context: A080618 A082136 A153596 this_sequence A006469 A081905 
               A016138
%Y A056986 Adjacent sequences: A056983 A056984 A056985 this_sequence A056987 A056988 
               A056989
%K A056986 nonn
%O A056986 1,4
%A A056986 Eric Weisstein (eric(AT)weisstein.com)

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