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%I #6 Mar 31 2012 10:29:02
%S 1,7,34,182,1107,7773,62212,559948,5599525,61594835,739138086,
%T 9608795202,134523132919,2017846993897,32285551902472,548854382342168,
%U 9879378882159177,187708198761024543,3754163975220491050
%N Operation count to create all permutations of n distinct elements using Algorithm L (lexicographic permutation generation) from Knuth's The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of loop repetitions in reversal step.
%D D. E. Knuth: The Art of Computer Programming, Volume 4, Combinatorial Algorithms, Volume 4A, Enumeration and Backtracking. Pre-fascicle 2B, A draft of section 7.2.1.2: Generating all permutations. Available online; see link.
%H D. E. Knuth, <a href="http://www-cs-faculty.stanford.edu/~knuth/fasc2b.ps.gz">TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations)</a>.
%H <a href="http://www.randomwalk.de/sequences/lpure.txt">FORTRAN implementation of Knuth's Algorithms L for lexicographic permutation generation</a>.
%F a(2)=1, a(n)=n*a(n-1) + (n-1)*floor[(n+1)/2] for n>=3. c = limit n --> infinity a(n)/n! = 1.54308063481524377826 = (e+1/e)/2 a(n) = floor [c*n!-(n+1)/2] for n>=2.
%o FORTRAN program available at link.
%Y Cf. A038155, A038156, A056542, A080047, A080049, A079755.
%K nonn
%O 2,2
%A _Hugo Pfoertner_, Jan 24 2003
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