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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 Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy] INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 565 FORMULA a(n) = 2^n*(n-1)! for n>1. E.g.f.: (1+2x)/(1-2x). - 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) = 2n 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 January 19 19:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)