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A046224
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Distinct numbers seen when writing first numerator and then denominator of central elements of 1/2-Pascal triangle.
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3
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1, 2, 3, 11, 40, 147, 546, 2046, 7722, 29315, 111826, 428298, 1646008, 6344366, 24515700, 94942620, 368404110, 1431985635, 5574725970, 21732560850, 84828633120, 331488081210, 1296712152060, 5077282282020, 19897457591700, 78039200913102, 306302623291476
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OFFSET
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1,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..200
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FORMULA
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a(n) = Sum_{k=1..n-2} (2*k+1)*binomial(2*n-k-5,n-3), n>2; a(1)=1, a(2)=2. - Vladimir Kruchinin, Sep 27 2011
a(n) = (5*n-9)/(8*n-12)*binomial(2*n-2,n-1), n>2; a(1)=1, a(2)=2. - Eric Werley, Sep 16 2015
G.f.: (3/2)*x^2 + (2*x - 3*x^2)/(2*sqrt(1-4*x)). - G. C. Greubel, Sep 24 2015
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EXAMPLE
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1/1; <-- hence 1;
1/1 1/1;
1/1 1/2 1/1; <-- hence 2
1/1 3/2 3/2 1/1;
1/1 5/2 3/1 5/2 1/1; <-- hence 3
1/1 7/2 11/2 11/2 7/2 1/1;
1/1 9/2 9/1 11/1 9/1 9/2 1/1; <-- hence 11
1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1;
...
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MATHEMATICA
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Join[{1, 2}, Table[(5 n - 9)/(8 n - 12) Binomial[2 n - 2, n - 1], {n, 3, 40}]] (* Vincenzo Librandi, Sep 24 2015 *)
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PROG
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(Magma) [1, 2] cat [(5*n-9)/(8*n-12)*Binomial(2*n-2, n-1): n in [3..40]]; // Vincenzo Librandi, Sep 24 2015
(PARI) a(n) = if (n<3, n, (5*n-9)/(8*n-12)*binomial(2*n-2, n-1));
vector(40, n, a(n)) \\ Altug Alkan, Oct 01 2015
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CROSSREFS
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Cf. A046213.
Sequence in context: A007756 A000280 A249402 * A081173 A179266 A265779
Adjacent sequences: A046221 A046222 A046223 * A046225 A046226 A046227
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KEYWORD
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nonn
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AUTHOR
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Mohammad K. Azarian
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EXTENSIONS
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More terms from James A. Sellers, Dec 13 1999
a(26)-a(27) from Vincenzo Librandi, Sep 24 2015
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STATUS
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approved
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