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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 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. 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-François 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)!<

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