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 A052714 a(0)=0; thereafter a(n) = Catalan(n-1)*2^(n-1)*n!. 12
 0, 1, 4, 48, 960, 26880, 967680, 42577920, 2214051840, 132843110400, 9033331507200, 686533194547200, 57668788341964800, 5305528527460761600, 530552852746076160000, 57299708096576225280000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n+1) is the number of square roots of any permutation in S_{8*n} whose disjoint cycle decomposition consists of 2*n cycles of length 4. - Luis Manuel Rivera Martínez, Feb 26 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 670 Jesús Leaños, Rutilo Moreno, and Luis Manuel Rivera-Martínez, On the number of mth roots of permutations, arXiv:1005.1531 [math.CO], 2010-2011. Jesús Leaños, Rutilo Moreno, and Luis Manuel Rivera-Martínez, On the number of mth roots of permutations, Australas. J. Combin. 52 (2012), 41-54 (Theorem 1). FORMULA E.g.f.: 1/4-1/4*(1-8*x)^(1/2). Recurrence: {a(1)=1, (4-8*n)*a(n)+a(n+1) = 0}. a(n) = A052701(n)*n!. a(n) = 8^(n-1)*GAMMA(n-1/2)/Pi^(1/2), n>0. a(n+1) = A090802(2n, n). - Ross La Haye, Oct 18 2005 a(n) = 2^(n-1)*(2*n-2)!/(n-1)! for n>=1. E.g.f. A(x) satisfies differential equation A'(x)=1/(1-4*A(x)). [Vladimir Kruchinin, May 04 2011] G.f.: x/(1-4x/(1-8x/(1-12x/(1-16x/(1-20x/(1-24x/(1-28x/(1-32x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012 G.f.: 2*x/G(0), where G(k)= 1 + 1/(1 - 2*x*(8*k+4)/(2*x*(8*k+4) - 1 + 16*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013 MAPLE spec := [S, {B=Union(Z, C), S=Union(B, C), C=Prod(S, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 3, 5!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *) Join[{0}, Table[CatalanNumber[n-1] 2^(n-1) n!, {n,  1, 20}]] (* Vincenzo Librandi, Mar 11 2013 *) PROG (PARI) a(n)=if(n<1, 0, 2^(n-1)*(2*n-2)!/(n-1)!) (MAGMA) [0] cat [Catalan(n-1)*2^(n-1)*Factorial(n): n in [1..20]]; // Vincenzo Librandi, Mar 11 2013 CROSSREFS Cf. A000108, A221953, A221954. Essentially the same as A144828. Catalan(n-1)*M^(n-1)*n! for M=1,2,3,4,5,6: A001813, A052714 (or A144828), A221954, A052734, A221953, A221955. Sequence in context: A192260 A162676 A141119 * A144828 A138448 A071221 Adjacent sequences:  A052711 A052712 A052713 * A052715 A052716 A052717 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS Edited by N. J. A. Sloane, Feb 03 2013 STATUS approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)