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

1,3

Links

Table of n, a(n) for n=1..24.

C. G. Bower, Transforms (2)

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]

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 *)

Crossrefs

Central column of triangle A034877.

Sequence in context: A084154 A265836 A083099 * A328039 A264960 A151019

Adjacent sequences: A032092 A032093 A032094 * A032096 A032097 A032098

Keyword

nonn

Author

Christian G. Bower

Status

approved