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A032184 "CIJ" (necklace, indistinct, labeled) transform of 1, 3, 5, 7,... 12
1, 4, 16, 96, 768, 7680, 92160, 1290240, 20643840, 371589120, 7431782400, 163499212800, 3923981107200, 102023508787200, 2856658246041600, 85699747381248000, 2742391916199936000, 93241325150797824000, 3356687705428721664000, 127554132806291423232000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

C. G. Bower, Transforms (2).

Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]

Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 565.

Index entries for sequences related to necklaces

FORMULA

a(n) = 2^n*(n-1)! for n > 1.

E.g.f.: (1 + 2*x)/(1 - 2*x). - Paul Barry, May 26 2003 [This e.g.f. yields the sequence (a(n+1): n >= 0). - M. F. Hasler, Jan 15 2017]

a(n) + 2*(-n+1)*a(n-1) = 0. - R. J. Mathar, Nov 30 2012 [Valid for n >= 3; equivalently: a(n+1) = 2*n*a(n) for n > 1. - M. F. Hasler, Jan 15 2017]

G.f.: G(0) - 1, where G(k) = 1 + 1/(1 - 1/(1 + 1/(2*k + 2)/x/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 14 2013

Let s(n) = Sum_{k >= 1} 1/(2*k - 1)^n with n > 1, then s(n) = (-1)^n*PolyGamma(n-1, 1/2)/a(n). - Jean-Fran├žois Alcover, Dec 18 2013

MAPLE

A032184:=n->if n>1 then 2^n*(n-1)! else 1 fi: seq(A032184(n), n=1..30); # Wesley Ivan Hurt and M. F. Hasler, Jan 15 2017

MATHEMATICA

lst={1}; Do[AppendTo[lst, 2^n*(n-1)! ], {n, 2, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

Join[{1}, Table[2^n (n-1)!, {n, 2, 20}]] (* Harvey P. Dale, Oct 08 2017 *)

PROG

(PARI) apply( A032184=n->(n-1)!<<n-(n==1) , [1..18]) \\ M. F. Hasler, Jan 15 2017

CROSSREFS

Apart from the initial term, same as A066318.

Sequence in context: A317998 A027745 A293143 * A130683 A111976 A236772

Adjacent sequences:  A032181 A032182 A032183 * A032185 A032186 A032187

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified April 19 00:03 EDT 2021. Contains 343098 sequences. (Running on oeis4.)