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 A001540 Number of transpositions needed to generate permutations of length n. (Formerly M1856 N0734) 2
 0, 2, 8, 36, 184, 1110, 7776, 62216, 559952, 5599530, 61594840, 739138092, 9608795208, 134523132926, 2017846993904, 32285551902480, 548854382342176, 9879378882159186, 187708198761024552, 3754163975220491060, 78837443479630312280, 1734423756551866870182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from T. D. Noe) R. J. Ord-Smith, Generation of permutation sequences: Part 1, Computer J., 13 (1970), 151-155. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. FORMULA E.g.f.: cosh(x)/(1-x) - exp(x). Recurrence: a(n) = n*a(n-1) + n - (n mod 2). a(n) = -1 + n!*Sum{k=0..floor(n/2)} 1/(2*k)! = -1 + round(n! * cosh(1)). a(n) = |A009179(n)| - 1 = (n-1)*|A009179(n-1) - A009179(n-2)|. a(n) ~ [cosh(1)*n!] - 1, where [x] is the floor of x. - Simon Plouffe, Nov 28 2018 EXAMPLE a(5)=-1+5!(1+1/2!+1/4!)=-1+120+60+5=184. MAPLE a := n -> (exp(1)*GAMMA(1 + n, 1) + exp(-1)*GAMMA(1 + n, -1))/2 - 1: seq(simplify(a(n)), n=1..20); # Peter Luschny, Dec 05 2018 MATHEMATICA With[{nn=20}, Rest[CoefficientList[Series[Cosh[x]/(1-x)-Exp[x], {x, 0, nn}], x]Range[0, nn]!]] (* Harvey P. Dale, Mar 04 2013 *) PROG (PARI) a(n)=-1+n!*sum(k=0, floor(n/2), 1/(2*k)!) (J) a001540=:13 : '<:+/(!y)%!+:i.>:<.-:y' NB. Stephen Makdisi, May 02 2018 (MAGMA) [-1 + (&+[Factorial(n)/Factorial(2*k): k in [0..Floor(n/2)]]): n in [1..20]]; // G. C. Greubel, Nov 28 2018 (Sage) [-1 + factorial(n)*sum(1/factorial(2*k) for k in range(floor((n+2)/2))) for n in (1..20)] # G. C. Greubel, Nov 28 2018 (GAP) a:=[0];; for n in [2..20] do a[n]:=n*a[n-1]+n-(n mod 2); od; a; # Muniru A Asiru, Dec 05 2018 CROSSREFS Cf. A009179. Sequence in context: A081958 A316663 A243948 * A129044 A052582 A222468 Adjacent sequences:  A001537 A001538 A001539 * A001541 A001542 A001543 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Edited by Ralf Stephan, Apr 16 2004 STATUS approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)