

A032123


Number of 2nbead blackwhite reversible strings with n black beads.


2



1, 1, 4, 10, 38, 126, 472, 1716, 6470, 24310, 92504, 352716, 1352540, 5200300, 20060016, 77558760, 300546630, 1166803110, 4537591960, 17672631900, 68923356788, 269128937220, 1052049834576, 4116715363800
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OFFSET

0,3


COMMENTS

It appears that a(n) is also the number of quivers in the mutation class of affine B_n or affine type C_n for n>=2. [Christian Stump, Nov 02 2010]


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
C. G. Bower, Transforms (2)
N. J. A. Sloane, Classic Sequences


FORMULA

n odd: C(2n1, n1); n even: C(2n1, n1) + C(n1, n/21)
"BIK[ n ](2n1)" (reversible, indistinct, unlabeled, n parts, 2n1 elements) transform of 1, 1, 1, 1...
E.g.f.: exp(x)*cosh(x)*BesselI(0, 2*x).  Vladeta Jovovic, Apr 07 2005
G.f.: (1/2)*((14*x)^(1/2)+(14*x^2)^(1/2))  Mark van Hoeij, Oct 30 2011.
Conjecture: n*(n1)*a(n) 2*(n1)*(3*n4)*a(n1) +4*(2*n^214*n+19)*a(n2) +8*(n^2+5*n19)*a(n3) 16*(n3)*(3*n10)*a(n4) +32*(n4)*(2*n9)*a(n5)=0, n>5.  R. J. Mathar, Nov 09 2013
a(n) ~ 2^(2*n1)/sqrt(Pi*n).  Vaclav Kotesovec, Mar 29 2014


MATHEMATICA

With[{nn = 50}, CoefficientList[Series[Exp[x]*Cosh[x]*BesselI[0, 2*x], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Feb 15 2017 *)


CROSSREFS

Central column of Losanitsch's triangle A034851.
Sequence in context: A197051 A149191 A149192 * A149193 A149194 A149195
Adjacent sequences: A032120 A032121 A032122 * A032124 A032125 A032126


KEYWORD

nonn


AUTHOR

Christian G. Bower


STATUS

approved



