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%I #12 Dec 23 2020 15:00:52
%S 1,2,1,4,2,1,7,56,28,14,7,84,42,21,315,5040,2520,1260,630,315,6615,
%T 145530,72765,1746360,873180,436590,218295,6112260,3056130,1528065,
%U 47370015,1515840480,757920240,378960120
%N a(1) = 1. For n > 1, a(n) = a(n-1)/2 if a(n-1) is even, a(n) = a(n-1)*n otherwise.
%C Conjecture: The sequence is unbounded. - _Felix Fröhlich_, Aug 08 2017
%H Harvey P. Dale, <a href="/A290650/b290650.txt">Table of n, a(n) for n = 1..1000</a>
%t nxt[{n_,a_}]:={n+1,If[EvenQ[a],a/2,a(n+1)]}; NestList[nxt,{1,1},40][[All,2]] (* _Harvey P. Dale_, Dec 23 2020 *)
%o (PARI) terms(n) = my(x=1, k=1, i=0); while(1, if(i==n, break, if(i==0, print1(x, ", "); k++; i++, if(x%2==0, x=x/2; k++, x=x*k; k++); print1(x, ", "); i++)))
%o /* Print initial 40 terms as follows */
%o terms(40) \\ _Felix Fröhlich_, Aug 08 2017
%K nonn
%O 1,2
%A _John Bailey_, Aug 08 2017