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Positions of non-crossing fixed-point-free involutions encoded by A014486 in A055089. Permutation of A064640.
3

%I #5 May 01 2014 02:49:07

%S 0,1,7,23,127,415,143,659,719,5167,16687,5455,26815,28495,5183,16703,

%T 5699,36899,38579,5759,36959,40031,40319,368047,1174447,379567,

%U 1901647,1992367,368335,1174735,389695,2627455,2718175,391375,2629135,2799055

%N Positions of non-crossing fixed-point-free involutions encoded by A014486 in A055089. Permutation of A064640.

%p map(PermRevLexRank,map(NonCrossingTranspos, A014486));

%p NonCrossingTranspos := n -> convert(NonCrossingTransposAux(binexp2pars(n),1),'permlist',binwidth(n));

%p NonCrossingTransposAux := proc(s,ii) local e,p,i,j; i := ii; p := []; for e in s do p := permul(p,NonCrossingTransposAux(e,i+1)); j := i+CountParens(e)+1; p := permul(p,[[i,j]]); i := j+1; od; RETURN(p); end;

%p CountParens := proc(s) local e,k; if(0 = nops(s)) then RETURN(0); fi; e := 0; for k in s do e := e+2+CountParens(k); od; RETURN(e); end;

%Y Maple procedure binexp2pars given in A057501, permul in A060125.

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 02 2001