A032095 Number of reversible strings with n-1 black beads and n-1 white beads. String is not palindromic.

1, 1, 2, 10, 32, 126, 452, 1716, 6400, 24310, 92252, 352716, 1351616, 5200300, 20056584, 77558760, 300533760, 1166803110, 4537543340, 17672631900, 68923172032, 269128937220, 1052049129144, 4116715363800

Offset: 1

Author

Christian G. Bower

Keywords

• nonn

Links

• C. G. Bower, Transforms (2)

Crossrefs

Central column of triangle A034877.

Programs

Mathematica

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 *)

Formula

"BHK[ n ](2n-1)" (reversible, identity, unlabeled, n parts, 2n-1 elements) transform of 1, 1, 1, 1...

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)

E.g.f. : 1+exp(x)*sinh(x)*BesselI(0,2x). [From Paul Barry, Aug 11 2009]