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A032095 Number of reversible strings with n-1 black beads and n-1 white beads. String is not palindromic. 1
1, 1, 2, 10, 32, 126, 452, 1716, 6400, 24310, 92252, 352716, 1351616, 5200300, 20056584, 77558760, 300533760, 1166803110, 4537543340, 17672631900, 68923172032, 269128937220, 1052049129144, 4116715363800 (list; graph; refs; listen; history; text; internal format)
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 * A264960 A151019 A004028

Adjacent sequences:  A032092 A032093 A032094 * A032096 A032097 A032098

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)