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%I #13 Sep 12 2013 12:26:09
%S 1,1,2,10,32,126,452,1716,6400,24310,92252,352716,1351616,5200300,
%T 20056584,77558760,300533760,1166803110,4537543340,17672631900,
%U 68923172032,269128937220,1052049129144,4116715363800
%N Number of reversible strings with n-1 black beads and n-1 white beads. String is not palindromic.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%F "BHK[ n ](2n-1)" (reversible, identity, unlabeled, n parts, 2n-1 elements) transform of 1, 1, 1, 1...
%F for n>1 a(n)=(1/2)*C(2n-2, n-1) if n is even, a(n)=(1/2)[C(2n-2, n-1)-C(n-1, (n-1)/2)] if n is odd. (_Emeric Deutsch_ Jul 25 2002)
%F E.g.f. : 1+exp(x)*sinh(x)*BesselI(0,2x). [From _Paul Barry_, Aug 11 2009]
%t Join[{1},Table[If[EvenQ[n],Binomial[2n-2,n-1]/2,(Binomial[2n-2,n-1]- Binomial[ n-1,(n-1)/2])/2],{n,2,30}]] (* _Harvey P. Dale_, Sep 12 2013 *)
%Y Central column of triangle A034877.
%K nonn
%O 1,3
%A _Christian G. Bower_
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