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 A081125 a(n) = n! / floor(n/2)!. 5
 1, 1, 2, 6, 12, 60, 120, 840, 1680, 15120, 30240, 332640, 665280, 8648640, 17297280, 259459200, 518918400, 8821612800, 17643225600, 335221286400, 670442572800, 14079294028800, 28158588057600, 647647525324800, 1295295050649600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Product of the largest parts in the partitions of n+1 into exactly two parts, n > 0. - Wesley Ivan Hurt, Jan 26 2013 (Clarified on Apr 20 2016) REFERENCES Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 FORMULA E.g.f.: (1+x)*exp(x^2). - Vladeta Jovovic, Sep 24 2003 From Peter Luschny, Aug 07 2009: (Start) a(n) = sqrt(n!*n\$) where n\$ denotes the swinging factorial (A056040). a(n) = 2^n Gamma((n+1+(n mod 2))/2)/sqrt(Pi). (End) E.g.f.: E(0) where E(k) = 1 + x/(1 - x/(x + (k+1)/E(k+1))) ; (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Sep 20 2012 G.f.: G(0) where G(k) =  1 + x*(2*k+1)/(1 - 2*x/(2*x + 1/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 18 2012 Conjecture: a(n) +2*a(n-1) -2*n*a(n-2) +4*(-n+2)*a(n-3) = 0. - R. J. Mathar, Nov 26 2012 From Wesley Ivan Hurt, Jun 06 2013: (Start) a(n) = n!/(n-floor((n+1)/2))!. a(n) = Product_{i = ceiling(n/2)..(n-1)} i. [Note: empty product = 1] a(n) = P( n, floor((n+1)/2) ), where P(n,k) are the number of k-permutations of n objects. (End) a(n) = n\$*floor(n/2)! where n\$ denotes the swinging factorial (A056040). - Peter Luschny, Oct 28 2013 EXAMPLE a(3) = 6 since 3+1 = 4 has two partitions into two parts, (3,1) and (2,2), and the product of the largest parts is 6. - Wesley Ivan Hurt, Jan 26 2013 (Clarified on Apr 20 2016) MAPLE Method 1)  a:=n->n!/floor(n/2)!; seq(a(k), k=0..40); # Wesley Ivan Hurt, Jun 03 2013 Method 2)  with(combinat, numbperm); seq(numbperm(k, floor((k+1)/2)), k = 0..40); # Wesley Ivan Hurt, Jun 06 2013 MATHEMATICA Table[n!/Floor[n/2]!, {n, 0, 30}] (* Wesley Ivan Hurt, Apr 20 2016 *) PROG (MAGMA) [Factorial(n)/(Factorial(Floor(n/2))): n in [0..30]]; // Vincenzo Librandi, Sep 13 2011 (PARI) a(n)=n!/(n\2)! \\ Charles R Greathouse IV, Sep 13 2011 (Sage) def a(n): return rising_factorial(ceil(n/2), floor(n/2)) [a(n) for n in range(26)]  # Peter Luschny, Oct 09 2013 CROSSREFS Cf. A004526, A056040, A081123. Sequence in context: A191836 A072486 A096123 * A138570 A161887 A139315 Adjacent sequences:  A081122 A081123 A081124 * A081126 A081127 A081128 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 07 2003 STATUS approved

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Last modified May 22 07:30 EDT 2019. Contains 323478 sequences. (Running on oeis4.)