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A110695
Kekulé numbers for certain benzenoids of trigonal symmetry.
1
1, 9, 341, 14859, 671509, 31816259, 1575219491, 80813149559, 4262996933909, 229858972288659, 12613108252122091, 702092835479959559, 39548041458039952291, 2250117073947022121799, 129122621276859925669799
OFFSET
0,2
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 313).
LINKS
FORMULA
a(n) = (2*binomial(2*n,n) - 1)*(binomial(2*n,n)^2 - binomial(2*n,n) + 1).
G.f.: 3/sqrt(1 - 4*x) - 1/(1 - x) + (8*EllipticK((1/2)*(1 - sqrt(1 - 64*x)))^2)/Pi^2 - (6*EllipticK(16*x))/Pi. - G. C. Greubel, Sep 06 2017
MAPLE
a:=n->(2*binomial(2*n, n)-1)*(binomial(2*n, n)^2-binomial(2*n, n)+1); seq(a(n), n=0..16);
MATHEMATICA
Table[(2*Binomial[2*n, n] - 1)*(Binomial[2*n, n]^2 - Binomial[2*n, n] + 1), {n, 0, 50}] (* G. C. Greubel, Sep 06 2017 *)
PROG
(PARI) for(n=0, 25, print1((2*binomial(2*n, n) - 1)*(binomial(2*n, n)^2 - binomial(2*n, n) + 1), ", ")) \\ G. C. Greubel, Sep 06 2017
CROSSREFS
Sequence in context: A098650 A354689 A098652 * A157589 A055601 A225328
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 03 2005
STATUS
approved